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Abstract This article introduces a unified criterion for input‐to‐state stability (ISS), integral input‐to‐state stability (iISS) and ‐input‐to‐state stability (‐ISS) of impulsive stochastic system with switching. The criterion demonstrates that the premise of a switching‐impulse system to achieve three types of ISS is that a mutually constraining relationship between switching, impulse and continuous dynamics needs to be satisfied. Furthermore, using it we know that switching can stabilize a system containing stabilizing factors by affecting both continuous dynamics and impulses, that switching itself is one of the factors in system instability, and that impulses have a dual effect on the stability of the system. The coefficients of the upper bound of Lyapunov functional differential operators are time‐varying functions and the impulses contain stable and unstable impulses, including the case of constants, which advances and improves the existing results. Finally, an example and its simulation results are given to verify the validity of theoretical analysis.
Kuang et al. (Mon,) studied this question.