Publisher: Taylor & Francis Journal: 10.1080/00207179.2018.1490820 DOI: International Journal of Control
Interval observer design for continuous-time switched systems under known switching and unknown inputs H. Ethabeta,* , T. Ra¨ıssib , M. Amairia , C. Combastelc and M. Aouna a
Research Laboratory Modeling, Analysis and Control of Systems (MACS), LR16ES22, National Engineering School of Gabes, University of Gabes, 6029 Gabes,Tunisia; b Conservatoire National des Arts et Metiers (CNAM), Cedric-Lab 292, Rue St-Martin, 75141 Paris Cedex 03, France; c IMS, Univ. Bordeaux, Bordeaux INP, CNRS UMR 5218, 351 cours de la lib´eration, 33405 Talence c´edex, France; * Corresponding Author’s Email:
[email protected] Received 27 Oct 2017, Revised 12 Apr 2018, Accepted 11 Jun 2018 ARTICLE HISTORY Compiled June 18, 2018 ABSTRACT This paper deals with unknown input estimation for switched linear systems in an Unknown But Bounded Error (UBBE) framework. Based on a known switching signal and under the fulfillment of the relative degree property by all the subsystems, a decoupling method is used to make the state partially affected by the unknown input. Assuming that the disturbances and the measurement noises are unknown but bounded with a priori known bounds, lower and upper bounds of the unmeasured state and unknown input are then computed. A numerical example illustrates the efficiency of the proposed methodology. KEYWORDS Unknown input, interval estimation, state transformation, continuous-time switched systems.
1.
Introduction
Switched systems have appeared as an important class of Hybrid Dynamical Systems (HDSs) and raise interesting theoretical challenges. They consist of a family of continuous or discrete-time subsystems and a switching rule governing the switching among them. At each time, only one subsystem is active. Several works treated switched systems such as (Djemai & Defoort, 2015; Liberzon, 2012; Branicky, 1998; Ping, Lee, & Shim, 2017). Stability and control problems have been widely studied during the last decades. For the stability analysis of switched systems, a common Lyapunov function and multiple Lyapunov functions were introduced in (Hu, Zhai, & Michel, 2002) and (Liberzon & Morse, 1999) respectively. Also, dwelltime based approaches were developed in (Hetel, 2007; Serres, Vivalda, & Riedinger, 2011) and the references therein for the derivation of stability conditions. State estimation of switched systems without unknown input has been tackled in some studies such as (Birouche, Daafouz, & Iung, 2006; Arichi, Djemai, Cherki, & Manamanni, 2015).
