Sliding mode control for switched nonlinear systems under asynchronous switching

In this paper, an integral sliding mode control approach is employed to analyze the mean-square exponential stability for a class of uncertain switched nonlinear stochastic systems under asynchronous switching signals. Firstly, an integral sliding surface is designed and a sufficient condition for its existence are presented to guarantee the mean-square exponential stability of switched systems in the sliding motion. Then variable controllers are designed such that switched systems remain in the sliding motion from the initial time instant. Due to the asynchronous switching between system modes and the corresponding controllers, the results presented allow the closed-loop systems to be unstable in the mismatched periods. Finally, a numerical example is presented to illustrate the effectiveness of the proposed results.