Input-to-state stability for nonlinear systems with stochastic impulses

In this study, the problem of input-to-state stability (ISS) is systematically investigated for nonlinear systems with stochastic impulses. First, the ISS problem is considered for systems, where impulsive strengths are assumed to be stochastic and impulsive intervals are confined by the average impulsive interval. Then, the ISS problem is analyzed for nonlinear systems with both stochastic impulsive intensity and density. Several different cases are considered, i.e., cases where the impulsive instants are satisfied by a renewal process, Poisson process, semi-Markov chain and Markov chain. An example of coordination of multi-agent systems is provided to illustrate the effectiveness of the proposed new stability criteria.Yang Tang, Xiaotai Wu, Peng Shi, Feng Qia