Hybrid [formula omitted]-gain performance analysis and synthesis of hybrid positive systems

Abstract

This paper addresses the analysis and synthesis of hybrid positive systems with hybrid L1×ℓ1-gain performance. The considered systems contain both continuous- and discrete-time positive subsystems. The notion of hybrid L1×ℓ1-gain performance is introduced for hybrid positive systems. First, some sufficient conditions for the stability of the system without disturbances are established using a hybrid copositive Lyapunov function incorporated with average dwell time switching. Then, the characterization on the stability with hybrid L1×ℓ1-gain performance of the system with continuous- and discrete-time disturbances is explored based on linear programming. A hybrid average dwell time switching law is proposed, where continuous- and discrete-time subsystems have their own average dwell time switching. Furthermore, a hybrid controller of the system is designed by virtue of matrix decomposition approach. Finally, one example is given to verify the validity of the results.