Abstract
In this paper, we focus on the stabilization of positive switched linear time-varying systems with delay. By constructing Lyapunov-Metzler inequalities, state-dependent switching signals have been designed such that the system is asymptotically stable, even if each subsystem is not asymptotically stable. Both the continuous-time and the discrete-time positive switched linear time-varying systems have been taken into consideration. Numerical examples are also given to verify the validity of our results.
Highlights
Switched system receives much attention in recent years [1]
It is well known that positive switched system has wide applications in practice, such as consensus of multi-agent systems [2], congestion control in communication networks [3], chemical reaction networks [4], drug delivery control in anesthesia [5] and Markovian jump systems [6], [7]
For the stabilization of positive switched linear systems (PSLSs), many people focused on the stabilization of the system under time-dependent switching [8]–[14]
Summary
Switched system receives much attention in recent years [1]. Positive switched system is a special switched system, which has the properties of positive systems, and the nature of switched systems. The authors in [22] and [23] studied the stabilization of continuous-time PSLSs under state-dependent switching by using common linear co-positive Lyapunov function and multiple linear co-positive Lyapunov functions, respectively, where a Hurwitz convex combination condition was proposed in [22]. Inspired by the works in [24]–[26], we will study the stabilization of continuous-time and discrete-time positive switched linear time-varying systems with delay. By introducing a piecewise linear copositive Lyapunov function, Lyapunov-Metzler inequalities have been established to determine the state-dependent switching signals under which the system is asymptotically stable. Sun: Stabilization of Positive Switched Linear Time-Varying Systems With Delay Under State-Dependent Switching.
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