Stability analysis for a class of random nonlinear impulsive systems

In this paper, the problem of noise-to-state stability (NSS) and globally asymptotic stability (GAS) is investigated for a class of nonlinear systems with random disturbances and impulses, where the random noises have finite second-order moments and the so-called random impulses mean that impulse ranges are driven by a sequence of random variables. First, some general conditions are given to guarantee the existence and uniqueness of solutions to random nonlinear impulsive systems. Next, when the continuous dynamics are stable but the impulses are destabilizing, the NSS and GAS of random nonlinear impulsive systems are examined by the average impulsive interval approach. Then, when the continuous dynamics are unstable but the impulses are stabilizing, it is shown that the NSS and GAS can be retained by using the reverse average impulsive interval approach. Finally, the theoretical findings are substantiated with illustrative examples.