This paper firstly discusses the existence and boundedness of unique global solution for highly nonlinear switched stochastic systems (SSSs) with time delays, where the switching signal is deterministic switching signal. Although the existence and boundedness of unique global solution can be obtained under local Lipschitz condition and Khasminskii‐type condition, highly nonlinear SSSs with time delays may not be stable. Therefore, a delay feedback control function can be designed for studying the stability of highly nonlinear SSSs with time delays, whose coefficients do not satisfy the linear growth condition. By using the Mathematical induction, Lyapunov function approach and the average dwell time method, H∞ stability and the pth moment exponential stability are studied for highly nonlinear SSSs with time delays. An explanatory example is given to illustrate the effectiveness of the main results.

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