Robust exponential stabilization and L2‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

Abstract For the nonlinear continuous‐time switched system with input saturation under asynchronous switching action, the problem of actuator failure is investigated in the presence of external disturbances. Firstly, a sufficient condition for the robust exponential stabilization of system is obtained by using the minimum dwell‐time method combining the piecewise Lyapunov function method. Secondly, a sufficient condition for the tolerance disturbances of the system is obtained by using the similar approach. Thirdly, the weighted ‐gain is analysed. Then, we maximize the estimation of the domain of attraction for the closed‐loop system by taking the shape of a set into consideration. Furthermore, the fault‐tolerant state feedback controllers are designed, which aim at enlarging the estimation of domain of attraction for the closed‐loop system and obtaining the maximum value of tolerance disturbance and the minimum upper bound on the weighted ‐gain. Last but not least, we give a numerical example to verify the effectiveness of the proposed approach and compare the state responses curve under the action of the fault‐tolerant and the standard controller.