LAUSR

This paper deals with the problems of finite-time $$L_2$$L2–$$L_\infty $$L∞ control for stochastic switched systems under asynchronous switching with time-varying delay and nonlinearity. Because of the presence of delay in the switching signal of controllers, the switching of the controllers is asynchronous with the switching of the subsystems. Firstly, based on average dwell time approach, merging switching signal technique and multiple Lyapunov function method, state feedback controllers are designed to guarantee the finite-time boundedness of stochastic switched time-delay systems under asynchronous switching by linearization techniques. Then the finite-time $$L_2$$L2–$$L_\infty $$L∞ performance is analyzed. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.