Comparison principles and input-to-state stability for stochastic impulsive systems with delays

Abstract

ABSTRACT In this paper, the input-to-state stability (ISS), the pth moment exponential ISS and the stochastic input-to-state stability issues are investigated for the stochastic impulsive systems with time delays via the comparison principle method. Firstly, several general comparison principles in vector-version are proposed guaranteeing the existence, uniqueness and magnitude for solutions of the addressed system. Then based on these established comparison principles, the ISS-related properties are investigated for the stochastic impulsive delayed model. Finally, one example is given to illustrate effectiveness of the obtained results.