Asynchronous rate anti-bump switching convex control for a class of switched positive linear systems

In this paper, the asynchronous rate anti-bump switching control issue for switched positive linear systems is addressed based on a novel Lyapunov function under admissible edge-dependent switching. Firstly, the definition of asynchronous rate anti-bump switching performance is proposed to restrain the rate bumps induced by system and controller mode switchings. A multiple convex copositive Lyapunov function is established for the asynchronously switched positive linear systems, allowing the Lyapunov function to descend at switching instants and largely relaxing the restriction conditions of the asynchronous rate anti-bump switching performance. Then, an asynchronous time-varying convex controller that depends on the time elapsed since the switching instant is devised, maintaining the last decided value of the former switching interval during the mismatched period. A group of sufficient conditions are developed to guarantee the asynchronous rate anti-bump switching performance of switched positive linear systems. Finally, a data communication network and a numerical example are provided to demonstrate how the switching performance of the system rate is improved effectively.