Extended Asynchronous Switching Control of Discrete-Time Switched Positive Linear Systems

An extended asynchronous switching control problem for a class of discrete-time switched positive linear systems is investigated in this paper. Different from the conventional asynchronous switching in the presence of only detection delay, the extended asynchronous switching stems from two aspects: detection delay and false alarm, which can better depict the practical situation in dynamic systems control. By resorting to the average dwell time approach, a state-feedback controller is designed to guarantee the resulting closed-loop system to be positive and exponentially stable. Unlike the existing results, the obtained condition permits the ascent of the multiple linear copositive Lyapunov functions caused by detection delay and false alarm, which is less conservative. Moreover, the case without false alarm is discussed. Finally, a simulation example is exploited to verify the validity of the proposed theoretical results.

1 Introduction

Positive systems whose states and outputs always remain nonnegative whenever both initial conditions and inputs take nonnegative values can be easily encountered in real world, for instance, power system chemical engineering, networks of reservoirs [1] and population dynamics [2], and so forth. However, the positive constraint of systems may give rise to invalidation of some existing results on general systems. Accordingly, positive systems have captured widespread attention of researchers in control community over the past few years. Meanwhile, some achievements for positive systems in theory and applications have been proposed [1, 3–5].