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This paper studies the input-to-state stability (ISS) and the finite-time input-to-state stability issues for the discrete-time stochastic switched nonlinear systems with time-varying delay. Based on the improved vector-version comparison principle and by employing the stochastic analysis method, sufficient conditions are first derived to guarantee the discrete-time stochastic switched system to be finite-time input-to-state stable in mean and finite-time stochastic input-to-state stable. Then, the comparison principle is further utilised to establish the  p -th moment ISS result. As an application, the mean-square ISS is analysed for the linear discrete-time stochastic switched system. At the end of the paper, two numerical examples are provided to illustrate the feasibility/effectiveness of the obtained results.

Finite-time input-to-state stability of discrete-time stochastic switched systems: a comparison principle-based method