On l₁ stability of switched positive singular systems with time‐varying delay

Abstract

SUMMARYThis paper investigates the problem of exponential stability and l 1 -gain performance analysis for a class of discrete-time switched positive singular systems with time-varying delay. Firstly, a necessary and sufficient condition of positivity for the system is established by using the singular value decomposition method. Then by constructing an appropriate co-positive Lyapunov functional and using the average dwell time scheme, we develop a sufficient delay-dependent condition and identify a class of switching signals for the switched positive singular system to be exponentially stable and meet a prescribed l 1 -gain performance level under the switching signal. Based on this condition, the decay rate of the system can be tuned and the optimal system performance level can be determined by solving a convex optimization problem. All of the criteria obtained in this paper are presented in terms of linear programming, which suggests a good scalability and applicability to high dimensional systems. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.

New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

“…Such time delays may degrade the performance, cause oscillation or even destroy stability of the system [4]. Therefore, analysis and synthesis problems for systems with time delays have become the focus of intensive research, including stability [5], [6], [7], control [8], filtering [9] for various systems such as stochastic system [10], singular system [11], positive system [12], fuzzy system [13]. Obviously, stability analysis for the linear systems with time delays is the foundation, and many researchers have focused on developing new techniques for analyzing the stability of systems with time delays because such techniques can be extended to synthesis problems in various systems with time delays.…”

Exponential stability of impulsive positive switched systems with discrete and distributed time‐varying delays

“…The effect of time delay on the system behavior is bidirectional: on the one hand, it may cause the degradation (or even instability) of system performance; on the other hand, in some control systems, it can be used to improve the control effect . Facts have been proved that the stability problem of positive switched systems with constant delay, time‐varying delays, or mixed (discrete and distributed) time‐varying delays can be solved well by the method of copositive Lyapunov‐Krasovskii functional. It should be pointed out that the derivative of time‐varying delays in the works of Liu et al and Li et al is restricted to less than 1.…”

A novel approach to L1 filter design for asynchronously switched positive linear systems with dwell time

“…Many results on the L 1 ‐gain analysis and synthesis problems of switched positive systems have been obtained. To mention a few, the L 1 ‐gain performance of switched positive singular systems with delays has been studied in the work of Li and Lin, the stability and L 1 ‐gain performance of switched positive linear systems (SPLSs) have been studied in the work of Xiang et al, and the robust stability and L 1 ‐gain performance of switched positive fuzzy systems have been investigated in the work of Li et al The readers can refer to the literature for further results.…”