Lecture Notes in Control and Information Sciences 375

Lecture Notes in Control and Information Sciences Editors: M. Thoma, M. Morari

375

Giorgio Bartolini, Leonid Fridman, Alessandro Pisano, Elio Usai (Eds.)

Modern Sliding Mode Control Theory New Perspectives and Applications

ABC

Series Advisory Board F. Allgöwer, P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis

Editors Giorgio Bartolini

Alessandro Pisano

Department of Electrical and Electronic Engineering University of Cagliari Piazza d’armi, Cagliari 09100, Cagliari Italy

Automatic Control Group Department of Electrical and Electronic Engineering DIEE University of Cagliari, Italy 09123 Piazza d’Armi, Cagliari Italy E-Mail: [email protected]

Leonid Fridman

Elio Usai

Departamento de Control Division de Ingenieria Elecitrica Facultad de Ingenieria Ciudad Universitaria Universidad Nacional Autonoma de Mexico 04510, Mexico D.F., Mexico

Department of Electrical and Electronic Engineering University of Cagliari Piazza d’armi, Cagliari 09100, Cagliari Italy

ISBN 978-3-540-79015-0

e-ISBN 978-3-540-79016-7

DOI 10.1007/978-3-540-79016-7 Lecture Notes in Control and Information Sciences

ISSN 0170-8643

Library of Congress Control Number: 2008923754 c 2008 

Springer-Verlag Berlin Heidelberg

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed in acid-free paper 543210 springer.com

To my wife Irene, to my mother Lucia, and to the memory of my father Giovanni. A.P.

Preface

This book is a collection of invited chapters covering several areas of modern sliding mode control theory. Preparing this book we tried to identify key contributions defining the theoretical and applicative state of the art of the sliding mode control theory and the most promising trends of the ongoing research activities. The contributions is divided in four main parts: Part Part Part Part

I: Basic Theory. II: Design Methods III: Observers and Fault Detection IV: Applications

The first part of the book (Part I: Basic Theory) is devoted to a collection of six mostly theoretical chapters addressing basic theoretical issues of sliding-mode based control systems. The first Chapter, by Giorgio Bartolini, Elisabetta Punta, and Tullio Zolezzi, presents new definitions of approximability for nonlinear second order sliding mode control systems including the comparison with the related known properties for first order sliding mode control methods. Sufficient conditions are obtained for second-order regularization, a sliding motion error estimate is derived, and some relevant examples are discussed. Chapter 2, by Igor Boiko, Leonid Fridman, Alessandro Pisano, and Elio Usai, develops a systematic approach to the chattering analysis in systems with second order sliding modes. Sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding Poincar´e maps. For linear systems driven by the second-order SMC “Generalized SubOptimal” algorithm, analysis tools based on the frequency-domain methods are developed. Examples of analysis, worked examples, and simulation results are given throughout the Chapter. Chapter 3, by Igor Boiko, studies sliding mode systems containing parasitic dynamics. A model of the chattering behaviour, and a full-order model of the averaged motions having the same order of the original system, are obtained via

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the use of the locus of a perturbed relay system (LPRS) method. The possibility of shaping of the plant frequency characteristic in order to achieve the desired frequency of chattering and to enhance the closed-loop performance is explored in the chapter. The fourth Chapter, by Arie Levant and Lela Alelishvili, deals with a survey of the most recent developments of homogeneity-based higher-order SMC theory. The “black-box” control problem, where the systems input-output relative degree is the unique available prior information for the controller design, is dealt with, and several solutions are recalled. The ”Nested” and ”Quasi-continuous” arbitrary-order sliding mode controllers are described. Next the output-feedback sliding-mode control problem is tackled via the combined use of the arbitraryorder SMC algorithms and finite time converging exact differentiators. The principles and applications of high-order integral sliding mode control is finally discussed. Chapter 5 by Yaodong Pan and Katsuhisa Furuta deals first with the design of a second-order invariant PR-sliding sector for continuous time systems. A quadratically stable sector-based VS control system is proposed, where an “inner” and “outer” sectors are introduced to let the control law be continuous and more easily implementable in practice. The proposed VS control algorithm is applied to control an inverted pendulum control system. Chapter 6 by Zbigniew Galiasa and Xinghuo Yu, performs a complete analysis of discretization behaviors of some Equivalent Control Based (ECB) SMC systems with relative degree higher than one using the Euler’s discretization. Former results for Euler-discretized ECB-SMC systems with relative degree one are reviewed. This paves the way to study the ECB-SMC systems with relative degree higher than one. Some theoretical results for the Euler’s discretization of ECB-SMC systems with relative degree one are used to analyse the ECB-SMC systems with arbitrary relative degree. The chapter is concluded by some comparisons with the existing results on continuous-time high-order SMC systems, where certain commonalities are observed. The second part of the book (Part II: Design Methods) is a collection of chapters covering recent design techniques addressing SMC problems for specific, challenging, classes of systems. This part contains a number of combined approaches merging different approaches (e.g., homogeneity-based, flatness and backstepping, fractional-order controllers) and SMC techniques. In the Chapter 7, by Christopher Edwards, Thierry Floquet, and Sarah Spurgeon, the classical restriction of sliding mode design approaches, namely to assume that the transfer function matrix between the driving signal and the measured output of interest must be minimum phase and relative degree one, is studied. The chapter demonstrates that the relative degree condition can be weakened if the nominal linear system used for the controller or observer design is combined with sliding-mode exact differentiators. Similar approach is also exploited for improved unknown-input reconstruction scheme. Simulation results for a ninth order nonlinear system which does not satisfy the usual relative degree one condition are presented.

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In the Chapter 8, by Simon Baev, Yuri Shtessel, and Ilya Shkolnikov, asymptotic output tracking in a class of causal nonminimum-phase uncertain nonlinear systems is addressed via higher order sliding mode approach. Local asymptotic stability of the output tracking-error dynamics is provided. An output reference profile and an external disturbance forcing the internal dynamics are defined by an unknown linear exosystem. The input-output dynamics is compensated by higher order sliding mode (HOSM) control. A numerical example illustrates the performance of the developed HOSM control algorithm. Chapter 9, by Isaac Chairez, Alexander Poznyak and Tatiana Poznyak, deals with the, so-called, neuro-tracking-control for a class of uncertain nonlinear dynamic systems subject to state and output external perturbations. Differential neural networks (DNN) are used to design the black-box nonlinear observer. Then, an adaptive (output based) HOSM controller using the current state estimate is suggested to realize the desired tracking process. A second-order mechanical system and a water ozonation process are considered as the illustrative examples. Chapter 10 by Hebertt Sira Ram´ırez and Vicente Feliu-Battle considers the control of a special class of Single Input Single Output (SISO) switched fractional order systems (SFOS) from the viewpoints of the Generalized Proportional Integral (GPI) control and sliding mode based modulator. Additionally, a Pulse Width Modulation (PWM) duty ratio synthesis approach is developed for the approximate discontinuous control of the same class of systems. A fractionalorder GPI controller is proposed which transforms the average model of the system into a “classical”, integer order, chain of integrators, with desired closed loop dynamics thus achieved through a classical compensation network robustly acting in the presence of constant load perturbations. An illustrative simulation example dealing with an electric radiator system is presented. In the Chapter 11 by Antonella Ferrara, Luisa Giacomini, and Claudio Vecchio, a class of nonholonomic systems in chained form, affected by uncertain nonlinear drift term and parametric uncertainties, is addressed. The proposed design methodology is based on a suitable transformation of the system model, so that, on the basis of the transformed system state, it is possible to design a particular sliding manifold and an appropriate parameter adaptation mechanism as well as to re-formulate the control problem as a second order sliding mode control problem. The capability of the proposed control law in dealing with unmatched parametric uncertainties, in contrast to previous proposals, is demonstrated. Chapter 12 by Jian-Xin Xu and Khalid Abidi considers the output tracking of a minimum-phase linear system subject to matched time varying disturbances. To accomplish the task of arbitrary reference tracking three approaches, based on discrete-time integral sliding mode (ISMC), will be considered: 1) State Feedback, 2) Output Feedback, and 3) Output Feedback with a State Observer. The proposed schemes allow full control of the closed-loop error dynamics and the elimination of the reaching phase. It is worth to highlight that the discrete-time

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ISMC can achieve the O(T 2 ) boundary for output tracking error even in the presence of O(T ) accuracy in the state estimation. Chapter 13 by Ali J Koshkouei, Keith Burnham, and Alan Zinober, investigates some connections between adaptive backstepping, flatness and sliding mode control. A combined technique using SMC and backstepping is presented to control a class of nonlinear uncertain perturbed systems which can be transformed into a parametric semi-strict feedback form. The concept of differential flatness and its exploitation in SMC design problems are also considered. The main advantages and limitations of backstepping, flatness and SMC are discussed by means of a simulation example. The third part of the book (Part III: Observers and Fault detection) concentrates on the topics of state observation and observer-based fault detection for some classes of inear and nonlinear processes. Both theoretical and applicative chapters are contained in this part of the book. In the Chapter 14 by Leonid Fridman, Arie Levant, and Jorge Davila algorithms for observation, identification and fault detection of linear time-invariant strongly observable systems with unknown inputs are developed, based on high order sliding modes. The possibility of their extension to strongly detectable and nonlinear systems is discussed. Some applications of the proposed algorithms are presented. In the Chapter 15, by Mehrdad Saif, Weitian Chen, and Qing Wu, the development of high order sliding mode observers and differentiator design strategies is reviewed. The design of a second order sliding mode observer and an highorder sliding mode differentiator is presented for state estimation in a class of nonlinear systems and for the real-time estimation of the derivatives of a signal function, respectively. Next, the proposed second order observer and the high order differentiators are applied together to fault diagnosis problems in systems with relative degree higher than one, and fault diagnosis schemes are constructed. Finally, two examples of application to fault diagnosis problems for uncertain systems are presented. Chapter 16 by Hassan Shraim, Mustapha Ouladsine, and Leonid Fridman concerns vehicle parameter and states estimation problems which are addresses via Sliding Mode Observers. The main contributions of the chapter resides in the estimation of the wheel contact forces with the ground, side slip angle and the velocity of the vehicle. Those estimations avoid the use of expensive sensors and allows to preview some critical situations that may occur while driving, such as excessive rotation around Z axis, excessive side slipping, inappropriate lateral acceleration. The proposed observers are simple to implement and guarantee fast convergence and robustness. They are validated by means of a high-order highly detailed vehicle simulator previously developed. The analysis covers most of the driving cases, such as a double lane trajectory, straight line motion with significant acceleration and deceleration, fast changes in the steering angle. The last Chapter 17, by Vincent Lebastard, Yannich Aoustin, Frank Plestan, and Leonid Fridman, suggests an alternative to the measurement of five-links biped robot absolute orientation, namely its estimation based on high order

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sliding mode observers. The measurement of the absolute orientation for a walking biped robot in imbalance phases is quite delicate. A solution for the estimation of the absolute orientation is proposed. The observer is based on a high order sliding mode differentiator, which has been chosen for its robustness, accuracy and finite-time convergence features. Stability analysis of observer-based control law and experimental results on the RABBIT biped robot prototype are displayed. The final, fourth part of the book (Part IV: Applications) presents some applicative chapters covering practical engineering control problems dealt with by means of the sliding mode approach. In the Chapter 18 by Yuri Orlov, Luis T. Aguilar, Leonardo Acho, and Adan Ortiz , orbital stabilization of a simple underactuated manipulator, namely, twolink pendulum robot (Pendubot) is under study. The quasi-homogeneous control synthesis is utilized to design a switched controller that drives the actuated link of the Pendubot to a periodic reference orbit in finite time. A modified Van der Pol oscillator is involved into the synthesis as an asymptotical generator of the periodic motion. The resulting closed-loop system is capable of moving from one orbit to another by simply changing the parameters of the modified Van der Pol oscillator. Performance issues of the proposed synthesis are illustrated in an experimental study of the swing up/balancing control problem of moving the Pendubot from its stable downward position to the unstable inverted position. Chapter 19 by Alexander Loukianov, Leonid Fridman, Jose Canedo, Edgar Sanchez, and Adolfo Soto-Cota, considers the combination of the block control principle and SM control techniques. A class of nonlinear minimum phase SISO systems presented in nonlinear block controllable (NBC) form, that models both the plant and actuator dynamics, is presented. Considering the complete plant and actuator dynamics, the block control technique is first used to suitably design the nonlinear sliding manifold, and the First Order Sliding Mode (FOSM) algorithm is implemented to ensure finite time convergence to the designed sliding manifold. Then a lower-order sliding manifold is designed based on the plant dynamics only, and a High Order Sliding Mode (HOSM) algorithm is implemented to achieve chattering free motion of the closed-loop system in the presence of the actuator unmodeled dynamics. The proposed method is applied to design robust controller for a power electric system in presence of the exciter system unmodeled fast dynamics. Finally neural network based second order SM block control for an electro-hydraulic system in presence of the electric actuator unmodeled dynamics is studied. Chapter 20 by Parisa Kaveh and Yuri Shtessel, studies the application of highorder SMC techniques to feedback-based glucose regulation in treatment of Diabetes. In the chapter, some higher order sliding mode control techniques are considered for the cascade robust stabilization of the glucose concentration level of a diabetic patient in presence of the parameter variations and meal disturbance. In the inner loop super-twisting control stabilizes the glucose pump-actuator. In the outer loop, the higher order sliding mode controller generates a command to the pump-actuator in terms of insulin injection rate. The efficiency of the proposed

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controllers together with the required HOSM based observers/differentiators, i.e. robustness and high accuracy, is confirmed via simulations. The concluding Chapter 21 by Alessandro Pisano and Elio Usai studies the contact force regulation problem in active pantographs for high-speed transportation systems. One of the main problems in high-speed-train transportation systems is indeed related to the current collection quality, that can dramatically decrease because of oscillations of the pantograph-catenary system. In the chapter some results about the possible implementation of Variable Structure Control (VSC) techniques on a wire-actuated symmetric pantograph are presented. Recent results about the frequency-based analysis of VSC systems featuring secondorder sliding modes are exploited to avoid the performance-destroying effect of the resonant wire actuator and to get a continuous control force without using observers. Simulations show that the contact force results to be satisfactorily close to the desired set-point also in the presence of measurement noise.

Cagliari, January 2008 Mexico City, January 2008 Cagliari, January 2008 Cagliari, January 2008

Giorgio Bartolini Leonid Fridman Alessandro Pisano Elio Usai

Contents

Part I: Basic Theory Regularization of Second Order Sliding Mode Control Systems Giorgio Bartolini, Elisabetta Punta, Tullio Zolezzi . . . . . . . . . . . . . . . . . . . . .

3

A Comprehensive Analysis of Chattering in Second Order Sliding Mode Control Systems Igor Boiko, Leonid Fridman, Alessandro Pisano, Elio Usai . . . . . . . . . . . . .

23

Analysis of Closed-Loop Performance and Frequency-Domain Design of Compensating Filters for Sliding Mode Control Systems Igor Boiko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

Discontinuous Homogeneous Control Arie Levant, Lela Alelishvili . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

Second-Order Sliding Sector for Variable Structure Control Yaodong Pan, Katsuhisa Furuta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

On Euler’s Discretization of Sliding Mode Control Systems with Relative Degree Restriction Zbigniew Galias, Xinghuo Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Part II: Design Methods Circumventing the Relative Degree Condition in Sliding Mode Design Christopher Edwards, Thierry Floquet, Sarah Spurgeon . . . . . . . . . . . . . . . . 137 HOSM Driven Output Tracking in the Nonminimum-Phase Causal Nonlinear Systems Simon Baev, Yuri B. Shtessel, Ilia Shkolnikov . . . . . . . . . . . . . . . . . . . . . . . . 159

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Contents

High Order Sliding Mode Neurocontrol for Uncertain Nonlinear SISO Systems: Theory and Applications Isaac Chairez, Alexander Poznyak, Tatyana Poznyak . . . . . . . . . . . . . . . . . . 179 A Generalized PI Sliding Mode and PWM Control of Switched Fractional Systems Hebertt Sira Ram´ırez, Vicente Feliu Battle . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Stabilization of Nonholonomic Uncertain Systems Via Adaptive Second Order Sliding Mode Control Antonella Ferrara, Luisa Giacomini, Claudio Vecchio . . . . . . . . . . . . . . . . . . 223 Output Tracking with Discrete-Time Integral Sliding Mode Control Xu Jian-Xin, Khalid Abidi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Flatness, Backstepping and Sliding Mode Controllers for Nonlinear Systems Ali J. Koshkouei, Keith Burnham, Alan Zinober . . . . . . . . . . . . . . . . . . . . . . 269

Part III: Observers and Fault Detection Observation and Identification Via High-Order Sliding Modes Leonid Fridman, Arie Levant, Jorge Davila . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 High Order Sliding Mode Observers and Differentiators– Application to Fault Diagnosis Problem Mehrdad Saif, Weitian Chen, Qing Wu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 Vehicle Parameter and States Estimation Via Sliding Mode Observers Hassan Shraim, Mustapha Ouladsine, Leonid Fridman . . . . . . . . . . . . . . . . . 345 An Alternative to the Measurement of Five-Links Biped Robot Absolute Orientation: Estimation Based on High Order Sliding Mode Vincent Lebastard, Yannick Aoustin, Franck Plestan, Leonid Fridman . . . 363

Part IV: Applications Robust Orbital Stabilization of Pendubot: Algorithm Synthesis, Experimental Verification, and Application to Swing up and Balancing Control Yuri Orlov, Luis T. Aguilar, Leonardo Acho, Ad´ an Ortiz . . . . . . . . . . . . . . . 383

Contents

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Higher Order SM Block-Control of Nonlinear Systems with Unmodeled Actuators: Application to Electric Power Systems and Electrohydraulic Servo-Drives Alexander G. Loukianov, Leonid Fridman, Jose M. Ca˜ nedo, Edgar Sanchez, Adolfo Soto-Cota . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 Blood Glucose Regulation Via Double Loop Higher Order Sliding Mode Control and Multiple Sampling Rate Parisa Kaveh, Yuri B. Shtessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427 Contact Force Regulation in Wire-Actuated Pantographs Alessandro Pisano, Elio Usai . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465

List of Contributors

Khalid Abidi Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576 [email protected] Leonardo Acho Centro de Investigaci´ on y Desarrollo de Tecnolog´ıa Digital, CITEDI-IPN, 2498 Roll Dr. #757, Otay Mesa, San Diego, CA, 92154 [email protected] Luis Aguilar Centro de Investigaci´ on y Desarrollo de Tecnolog´ıa Digital, CITEDI-IPN, 2498 Roll Dr. #757, Otay Mesa, San Diego, CA, 92154. [email protected] Lela Alelishvili Applied Mahematics Department, Tel-Aviv University, RamatAviv, Tel-Aviv 69978, Israel. [email protected] Yannick Aoustin Institut de Recherche en Communications et Cyberne´tique de Nantes, UMR CNRS 6597, Ecole Centrale de Nantes, Universit´e de

Nantes, Nantes, France. Yannick.Aoustin@ irccyn.ec-nantes.fr Giorgio Bartolini Department of Electrical and Electronic Engineering (DIEE), University of Cagliari, Piazza d’Armi, 09123, Cagliari (Italy). [email protected] Simon Baev Electrical and Computer Engineering Dept., The University of Alabama in Huntsville, 301 Sparkman Dr., Huntsville, AL, 35899 [email protected] Igor Boiko Department of Electrical and Computer Engineering, University of Calgary, 2500 University Dr. N.W., Calgary, Alberta, Canada. [email protected] Keith Burnham Control Theory and Applications Centre, Coventry University, Coventry CV1 5FB, UK, [email protected]

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List of Contributors

Jose M. Ca˜ nedo Centro de Investigaci´ on y de Estudios Avanzados del IPN, A. P. 31-438,C.P. 44550, Guadalajara, Jal., M´exico. [email protected] Isaac Chairez Department of Automatic Control CINVESTAV-IPN, AP. 14740, Av. Instituto Polit´ecnico Nacional No. 2508, C.P. 07360, Mexico D.F., Mexico. [email protected] Weitian Chen School of Engineering Science, Simon Fraser University, 8888 University Drive, Vancouver, British Columbia V5A 1S6 Canada. [email protected] Jorge Davila Department of Control, Engineering Faculty, National Autonomous University of Mexico (UNAM), 04510, Mexico, D.F., Mexico [email protected] Christopher Edwards Control and Instrumentation Research Group, University of Leicester, Leicester, LE1 7RH, UK [email protected] Vicente Feliu Battle Escuela T´ecnica Superior de Ingenieros Industriales, Universidad de Castilla La Mancha, Av. Camilo Jos´e Cela S/N, 13005 Ciudad Real, Espa˜ na [email protected] Antonella Ferrara Department of Computer Engineering and Systems Science, University of

Pavia, Via Ferrara 1, 27100 Pavia, Italy. [email protected] Thierry Floquet LAGIS UMR CNRS 8146, Ecole Centrale de Lille, BP 48, Cit´e Scientifique, 59651 Villeneuve-d’Ascq, France [email protected] Leonid Fridman Department of Control, Engineering Faculty, National Autonomous University of Mexico (UNAM), 04510, Mexico, D.F., Mexico [email protected] Katsuhisa Furuta Department of Computers and Systems Engineering, Tokyo Denki University, Hiki-gun, Saitama 350-0394, Japan. [email protected] Zbigniew Galias Department of Electrical Engineering, AGH University of Science and Technology, Krak´ ow, Poland. [email protected] Luisa Giacomini Eutecne Srl, Via Galata, 39/8 16121 Genova, Italy. [email protected] Parisa Kaveh Electrical and Computer Engineering Dept., The University of Alabama in Huntsville, 301 Sparkman Dr., Huntsville, AL, 35899 [email protected] Ali J Koshkouei Control Theory and Applications Centre, Coventry University, Coventry CV1 5FB, UK, [email protected]

List of Contributors

Vincent Lebastard Institut de Recherche en Communications et Cyberne´tique de Nantes, UMR CNRS 6597, Ecole Centrale de Nantes, Universit´e de Nantes, Nantes, France.

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Yaodong Pan The 21st COE Century Project Office, Tokyo Denki University, Ishisaka, Hatoyama, Hiki-gun, Saitama 350-0394, Japan [email protected]

[email protected]

Arie Levant Applied Mathematics Department, Tel-Aviv University, RamatAviv, Tel-Aviv 69978, Israel. [email protected] Alexander G. Loukianov Centro de Investigaci´ on y de Estudios Avanzados del IPN, A. P. 31-438,C.P. 44550, Guadalajara, M´exico. [email protected] Yuri Orlov CICESE Research Center, P.O. BOX 434944, San Diego, CA, 92143-4944, [email protected] Ad´ an Ortiz CICESE Research Center, P.O. BOX 434944, San Diego, CA, 92143-4944, [email protected]

Franck Plestan Institut de Recherche en Communications et Cyberne´tique de Nantes, UMR CNRS 6597, Ecole Centrale de Nantes, Universit´e de Nantes, Nantes, France. [email protected]

Alexander Poznyak Department of Automatic Control CINVESTAV-IPN, AP. 14740, Av. Instituto Politecnico Nacional No. 2508, C.P. 07360, Mexico D.F., Mexico. [email protected] Tatyana Poznyak Superior School of Chemical Engineering and Extractive Industries (ESIQIE-IPN), Edif. 7, UPALM, C.P. 07738, Mxico, D.F, Mxico [email protected]

Mustapha Ouladsine Laboratory of sciences of informations and of systems, SIS UMR 6168 University of Paul C´ezanne, Aix-Marseille III, Av escadrille de Normandie Niemen 13397 Marseille Cedex 20. [email protected]

Elisabetta Punta Institute of Intelligent Systems for Automation, National Research Council of Italy (ISSIA-CNR), Via De Marini, 6 - 16149 Genoa, Italy. [email protected]

Alessandro Pisano Department of Electrical and Electronic Engineering (DIEE), University of Cagliari, Piazza d’Armi, 09123, Cagliari (Italy) [email protected]

Mehrdad Saif School of Engineering Science, Simon Fraser University, 8888 University Drive, Vancouver, British Columbia V5A 1S6 Canada. [email protected]

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List of Contributors

Hebertt Sira Ram´ırez Cinvestav IPN, Av. IPN No. 2508, Departamento de Ingenier´ıa El´ectrica, Secci´on de Mecatr´ onica. Colonia Residencial Zacatenco AP 14740, 07300 M´exico D.F., M´exico. [email protected] Ilia Shkolnikov Z/I Imaging Corporation, an Intergraph Company, 230 Business Park Blvd., Madison, AL 35757 [email protected] Hassan Shraim Laboratory of sciences of informations and of systems, SIS UMR 6168 University of Paul C´ezanne, Aix-Marseille III, Av escadrille de Normandie Niemen 13397 Marseille Cedex 20. [email protected] Yuri B. Shtessel Electrical and Computer Engineering Dept., The University of Alabama in Huntsville, 301 Sparkman Dr., Huntsville, AL, 35899 [email protected] Edgar Sanchez Centro de Investigaci´ on y de Estudios Avanzados del IPN, A. P. 31-438,C.P. 44550, Guadalajara, Jal., M´exico. [email protected] Adolfo Soto-Cota Instituto Tecnol´ogico de Sonora, 5 de Febrero 818 sur, Cd. Obreg´ on, Sonora M´[email protected] Sarah Spurgeon Control and Instrumentation Research Group, University of Leicester, Leicester, LE1 7RH, UK [email protected]

Elio Usai Department of Electrical and Electronic Engineering (DIEE), University of Cagliari, Piazza d’Armi, 09123, Cagliari (Italy) [email protected] Claudio Vecchio Department of Computer Engineering and Systems Science, University of Pavia, Via Ferrara 1, 27100 Pavia, Italy. [email protected] Qing Wu School of Engineering Science, Simon Fraser University, 8888 University Drive, Vancouver, British Columbia V5A 1S6 Canada. [email protected] Jian-Xin Xu Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576 [email protected] Xinghuo Yu Platform Technologies Institute, RMIT University, Melbourne, VIC 3001, Australia [email protected] Alan Zinober Department of Applied Mathematics, The University of Sheffield, Sheffield S10 2TN, UK, [email protected] Tullio Zolezzi Department of Mathematics, University of Genoa, Via Dodecaneso, 35 - 16146 Genoa, Italy. [email protected]