Exponential Stability of Switched Positive Systems With Unstable Subsystems Based on Digraphs

Abstract

This paper addresses the transfer restricted switching problem for discrete-time switched positive linear systems with all unstable subsystems. To characterize the complex interaction between state components under subsystem switching, the switching digraph and state component digraph are conjoined and a novel switching walk approach is proposed to achieve the exponential stability of switched positive systems. By further deducing the relationship between the obtained decay rate of switched systems and the weight of the switching walk, an optimized stability result is presented and a switching cycle strategy is designed to make the decay rate of switched systems larger. Furthermore, a novel graph-based mode-dependent dwell time method is proposed, which allows subsystems to be activated at any integer multiple of a constant value. Finally, three simulation examples are provided to show the effectiveness of the proposed methods.