Finite-time stability and stabilization of switched nonlinear systems with asynchronous switching

This paper is concerned with the problem of finite-time stability and stabilization for switched nonlinear systems with asynchronous switching. Firstly, when not all subsystems are finite-time stable (FTS), we propose a finite-time stability criteria to show that if the constraint condition between the settling time and the average dwell time is satisfied, finite-time stability of the system is guaranteed. Then we extend the result to the case which Lipschitzian perturbations exist in the subsystems. When asynchronous switching is considered and not all closed-loop subsystems are finite-time stabilizable, we recur to the generalized inverse of matrices to design a state feedback controller to stabilize the original system. Finally, an example of two container liquid-level system is provided to illustrate the effectiveness of developed result.