New stabilization results for discrete-time positive switched systems with forward mode-dependent average dwell time

Abstract

The stability and stabilization of discrete-time linear positive switched systems are discussed in this paper. First, based on the concept of the forward mode-dependent average dwell time, a stability result for discrete-time linear positive switched systems is obtained by utilizing the multiple linear copositive Lyapunov functions. Then, by introducing multiple-sample Lyapunov-like functions variation, a new exponential stability result is derived. Finally, the conditions for the existence of mode-dependent stabilizing state feedback controllers are investigated, and two illustrative examples are given to show the correctness of the theoretical results obtained.

LP-based observer design for switched positive linear time-delay systems

“…The common characteristic of these systems is that their states are non-negative whenever the initial conditions are non-negative. Recently, switched positive linear systems consisting of positive linear systems and a switching signal have been paid much attention (Liu et al, 2017b; Shen and Wang, 2017). Dong and Chang (2017) proposed the asynchronous L 1 output tracking controller for switched positive linear systems.…”

Design of a stabilizing controller for discrete-time switched delay systems with affine parametric uncertainties

“…This signal may depend on time, state or both of them. Stability analysis and controller design of switched systems have attained much attention in the literature due to their widespread applications (Liu et al, 2015; Zhao et al, 2017; Zong et al, 2016). The procedure of controller design for switched systems includes three basic forms (Zhao et al, 2017): 1) controller design under arbitrary switching signals; 2) controller design under switching signals with some constraints; 3) design of stabilizing switching signals.…”

Observer-based H∞ finite-time control for switched linear systems with interval time-delay

“…ADT means that the number of switching instants in a finite interval is bounded and the average time between consecutive switching instants is not less than a constant. In the literature there are plenty of works considering suitable Lyapunov functionals to obtain an ADT bound that is as small as possible, for the stability and stabilization of switched systems (Briat, 2017; Cheng et al, 2015; Fei et al, 2017; Hespanha and Morse, 1999; Karabacak et al, 2014; Liu and Zhao, 2014; Liu et al, 2017; Ren et al, 2017; Shi et al, 2016; Xiang et al, 2017; Yuan and Wu, 2015).…”