Switching Signal Design for Exponential Stability of Uncertain Discrete-Time Switched Time-Delay Systems

Abstract

The switching signal design for exponential stability with ∞ performance of uncertain switched linear discrete-time systems with interval time-varying delay is considered. Systems with norm-bounded parameter uncertainties are considered. By taking a new Lyapunov-Krasovskii (LK) function, sufficient conditions for the existence of a class of stabilizing switching laws are derived in terms of linear matrix inequalities (LMIs) to guarantee the considered switched time-delay system to be exponentially stable. The resulting stability criteria are of fewer matrix variables and are less conservative than some existing ones. In addition, numerical examples are illustrated to show the main improvement.

Hyers–Ulam Stability, Exponential Stability, and Relative Controllability of Non‐Singular Delay Difference Equations

“…Kosmala and Teixeira [31] provided a good insight and discussed the behavior of solution of the difference equation of the type U k+1 � (A + U k−1 )/(BU k + U k−1 ). Liu et al [32] designed the exponential behavior of switch discrete-time delay system. Marwen and Sakly [33] discussed the stability techniques about the switched non-linear time-delay difference equations.…”

Asymptotic stability and stabilization of discrete‐time switched systems with time‐varying delay

“…Recently, many efforts have been made and many works have been done, by proposing several advanced techniques or by improving some existing results in the literature in order to study or to reduce the conservatism of different classes of switched systems. Either continuous case or discrete‐time case, are considered for whether switched linear systems without delay (SLs), for example, in References 18‐21, or switched linear systems with constant delay (SLTDs); see, for example, References 22‐28 or with time‐varying delay (SLTVDs); see References 4,7,9,23,29‐39. Specifically, stability and stabilization of such systems are studied.…”

A New AILC for a Class of Nonlinearly Parameterized Systems with Unknown Delays and Input Dead-Zone

“…The existence of time delays may make the controllers design more complicated and challenging, especially for systems with unknown time-delays. Stabilization problem of control systems with time delay has drawn much attention [28][29][30][31][32][33][34][35] due to its mathematical challenge and application demand in real-time control. In [28][29][30][31], the controller design and stability analysis for statedelayed systems were presented and [32][33][34][35] discussed the stabilization of systems with input delays.…”

“…Stabilization problem of control systems with time delay has drawn much attention [28][29][30][31][32][33][34][35] due to its mathematical challenge and application demand in real-time control. In [28][29][30][31], the controller design and stability analysis for statedelayed systems were presented and [32][33][34][35] discussed the stabilization of systems with input delays. In the field of ILC, although so many results have been obtained, only few ones were available for time-delay nonlinear systems [36][37][38][39][40][41], and the majority of these works were traditional iterative learning controllers.…”