Lyapunov-Krasovskii functionals for switched nonlinear input delay systems under asynchronous switching

This paper investigates the input-to-state stability for switched nonlinear input delay systems under asynchronous switching. Suppose a feedback control law has been designed such that the nominal closed-loop system is exponentially stable for a certain switching signal, and suppose further that a corresponding Lyapunov function for the nominal closed-loop system is available. In the presence of input delay and asynchronous switching, the system may not be stable under the same switching signal. For this case, we explicitly construct Lyapunov-Krasovskii functionals based on the knowledge of the known Lyapunov function. Then, by using the constructed Lyapunov-Krasovskii functionals, a new switching delay-dependent switching signal satisfying the new mode-dependent average dwell time conditions is provided to guarantee the input-to-state stability of the system with respect to the disturbance under a certain input delay bound. Two examples are given to illustrate the effectiveness of the proposed theory.