Reachability and controllability of switched linear discrete-time systems

Abstract

This paper investigates the reachability and controllability issues for switched linear discrete-time systems. Geometric characterization of controllability is presented. For reversible systems, the controllable sets and the reachable sets are identified in Wonham's geometric approach, and verifiable conditions for reachability and controllability are also presented.

A practical test for assessing the reachability of discrete-time Takagi–Sugeno fuzzy systems

“…where the N n x matrices M l k 0 l k 1 ···l k n x −1 are defined as in (20) (the notation M j is recovered by considering the bijection between the first J = N n x natural numbers and all the possible combinations of indices l k 0 , l k 1 , . .…”

“…The controllability of infinite dimensional systems has been studied in [9,10]. Further investigation has addressed the problem for stochastic [11,12,13,14], delayed [15,16], fractional [17,18,19] and switched [20,21,22,23] systems.…”

Reachability analysis of switched linear discrete singular systems

“…Remark 1 The main difference between R(π zj ) given in (8) and the reachable set of the normal switched linear systems given in [7] is that F…”

Stability of a Class of Hybrid Impulsive and Switching Systems

“…So far, most research work on hybrid systems has been devoted to stability analysis and stabilization, (Decarlo et al, 2000;Liberzon and Morse, 1999;Liberzon, 2003;Michel, 1999). Most recently, on the basis of Lyapunov functions and other analysis tools, the stability and stabilization for linear or nonlinear switched systems have been further investigated and many valuable results have been obtained (Daafouz et al, 2002;Ge et al, 2001;Ishii and Francis, 2002;Leonessa et al, 2001;Li et al, 2001;Mancilla-Aguilar, 2003), etc..…”

“…Hybrid systems consisting of interacting continuous and discrete dynamics under certain logic rules, have gained considerable attention in science and engineering (Aubin et al, 2001;Branicky, 1998;Decarlo et al, 2000;Ge et al, 2001;Hespanha and Morse, 1999;Li et al, 2001;Liberzon and Morse, 1999;Mancilla-Aguilar, 2003), since they provide a natural and convenient unified framework for mathematical modeling of many complex physical phenomena and practical applications. Examples include robotics, integrated circuit design, multi-media, manufac-turing, power electronics, switched-capacitor networks, chaos generators, automated highway systems and air traffic management systems.…”