LMI approach to exponential stability of linear systems with interval time-varying delays

Observer-based controller design of time-delay systems with an interval time-varying delay

“…(Phat et al, 2012) Given α > 0, the system (1), where u(t) = 0, is α-stable if there exists a positive number β > 0 such that every solution x(t, φ) satisfies the condition…”

“…There has been growing research interest in stability analysis and stabilization of systems subject to an interval Brought to you by | MIT Libraries Authenticated Download Date | 5/11/18 7:44 AM time-varying delay (see, for example, Botmart et al, 2011;Phat et al, 2012;Shao, 2009;Shao and Han, 2012). An interval time-varying delay is a time delay that varies within an interval whose lower bound is not restricted to be zero and its time derivative can even be undefined or unknown.…”

“…An interval time-varying delay is a time delay that varies within an interval whose lower bound is not restricted to be zero and its time derivative can even be undefined or unknown. Recently, exponential stability of linear systems with an interval time-varying non-differentiable delay was considered by Phat et al (2012). Also, the problem of designing memoryless state feedback controllers to exponentially stabilize a class of linear uncertain systems with an interval time-varying delay was studied by Botmart et al (2011).…”

New sufficient conditions for the asymptotic stability of discrete time-delay systems

“…A switched system with time-delay individual subsystems is called a switched time-delay system; in particular, when the subsystems are linear, it is then called a switched time-delay linear system. During the last decades, the stability analysis of switched linear continuous/discrete time-delay systems has attracted a lot of attention [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The main approach for stability analysis relies on the use of Lyapunov-Krasovskii functionals and linear matrix inequlity (LMI) approach for constructing a common Lyapunov function [19][20][21][22][23][24].…”

“…Although many important results have been obtained for switched linear continuoustime systems, there are few results concerning the stability of switched linear discrete systems with time-varying delays. It was shown in [5,7,11] that when all subsystems are asymptotically stable, the switching system is asymptotically stable under an arbitrary switching rule. The asymptotic stability for switching linear discrete time-delay systems has been studied in [10], but the result was limited to constant delays.…”