Global Exponential Stability and Stabilization of Fractional-Order Positive Switched Systems

Abstract

Abstract-This paper is concerned with the global exponential stability(GES) and stabilization of fractional-order positive switched systems(FOPSS) with average dwell time(ADT). Firstly, the the concept of GES is extended to FOPSS. Then, by constructing copositive Lyapunov functions and using ADT approach, a state feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is globally exponentially stable. Such conditions can be easily solved by linear programming. Finally, an example is given to demonstrate the effectiveness of the proposed method.Index Terms-fractional-order positive switched systems, global exponential stability, average dwell time, linear programming.

Finite-time stability and finite-time boundedness of fractional order switched systems

“…However, there are many differences between integer order systems and fractional order systems, which lead to different proof processes. We also know that FOSS are more complex and challenging (Cao et al, 2016; Liu et al, 2017a; Zhang et al, 2017), as also shown by the proof of Theorem 11.…”

“…FTS and stabilization of fractional order positive switched system are reported by Zhang et al (2017). Global exponential stability and stabilization of fractional order positive switched system are given by Cao et al (2016). These three papers are about positive switched systems.…”