Unknown Input Observers for Switched Nonlinear Discrete Time Descriptor Systems

Abstract

International audienceIn this paper, a linear matrix inequality (LMI) technique for state estimation of discrete-time, nonlinear switched descriptor systems is developed. The considered systems are composed of linear and nonlinear parts. An observer giving a perfect unknown input (UI) decoupled state estimation is proposed. Sufficient conditions of global convergence of observers are proposed. Numerical examples are given to illustrate this method

Observer Design for Switched Nonlinear System with Both Unknown Inputs and Measurement Noise

“…In the past decades, the stability, controllability and observer design of switched systems have been studied extensively [15][16][17][18][19][20][21]. However, in the field of switched system UIO designs, there are only a few results can be found in literature [22][23][24][25][26]. For example, in [22] Koenig et al investigated a class of discrete switched nonlinear system UIO design problems under arbitrary switching signal.…”

“…However, in the field of switched system UIO designs, there are only a few results can be found in literature [22][23][24][25][26]. For example, in [22] Koenig et al investigated a class of discrete switched nonlinear system UIO design problems under arbitrary switching signal. In [23], Bejarano et al proposed a reduced-order UIO design framework for a class of switched systems.…”

Observers design for switched discrete-time singular time-delay systems with unknown inputs

“…However, to the authors' knowledge, there are relatively few results reported on UI observers design for SSTDSs. It is worth noting that in Koenig et al's recent work [35], an unknown input decoupled observer was developed for discrete-time switched singular systems with UIs by employing the generalized inverse and LMI technique. Nevertheless, extension of the results in [35] to SSTDSs seems to be a nontrivial work since the observer must be redesigned to alleviate the adverse effect of time delays.…”

Discrete robust switched H∞ tracking state feedback controllers for lateral vehicle control

“…Therefore, a multiple model representation can easily be used. Consequently, the analysis and the synthesis of such systems involve the use of specific methods like adaptive methods (Narendra & Balakrishnan, 1997;Narendra, Driollet, Feiler, & George, 2003), gain-scheduled approaches (Apkarian, Gahinet, & Becker, 1995;Lawrence & Rugh, 1995;Leithead, 1999;Stilwell & Rugh, 1999), linear parameter varying systems (LPV) (Apkarian et al, 1995), Type-1 and Type-2 Fuzzy logic systems (Castillo & Melin, 2008;Mendel, 2004;Sugeno & Kang, 1988) and during the last decades the switched systems which constitute an important class of hybrid systems, have been introduced and widely developed (Branicky, 1998;Daafouz, Riedinger, & Iung, 2002;Deaecto, Geromel, & Daafouz, 2011;Geromel, Colaneri, & Bolzern, 2008;Koenig, Marx, & Jacquet, 2008;Koenig & Marx, 2009;Liberzon & Morse, 1999;Liberzon, 2003;Lin & Antsaklis, 2006Narendra & Balakrishnan, 1994;Sun & Ge, 2005). Such systems are defined by a finite number of local operating modes and a logical rule that manages switching between them.…”

“…Particularly, stability and stabilization problems of switched continuous-time and discrete-time linear systems were addressed in Narendra and Balakrishnan (1994), Liberzon and Morse (1999), Sun and Ge (2005), Lin and Antsaklis (2007), Lin and Antsaklis (2009), Branicky (1998), Daafouz et al (2002), Koenig et al (2008) and Du, Jiang, Shi, and Zhou (2007). The stability of other switched systems was also investigated such as switched linear and nonlinear descriptor systems (Koenig et al, 2008;Koenig & Marx, 2009), switched discrete-time systems with constant and timevarying delays (Du et al, 2007;Wu & Zheng, 2009), and recently switched linear systems with singular perturbation (Deaecto, Daafouz, & Geromel, 2012;Hachemi, Sigalotti, & Daafouz, 2012). Moreover, the readers are referred to the large surveys (Lin & Antsaklis, 2009;Sun & Ge, 2005), which emphasize that the literature on design of such systems is abundant.…”