Absolute exponential L1-gain analysis and synthesis of switched nonlinear positive systems with time-varying delay

This paper investigates absolute exponential stability and stabilization with L1-gain performance of switched nonlinear positive systems with time-varying delay. Nonlinear functions considered in the paper are located in a sector field and the time-varying delay is unknown but bounded. The notion of absolute exponential L1 stability of switched nonlinear positive systems is first introduced. A nonlinear Lyapunov–Krasovskii functional is constructed for the underlying systems. By using the Lyapunov–Krasovskii functional, a sufficient condition for absolute exponential L1 stability of the systems is established in terms of linear programming. Then, absolute exponential L1 control synthesis of the systems is addressed. A feedback control law containing nonlinear functions and a state-feedback control law are designed, respectively. By comparing with existing results, it is shown that the present design is less conservative. Finally, an illustrative example is provided to illustrate the effectiveness of the results.