Stability criteria of random nonlinear systems with non-instantaneous multiple impulse

This paper comprehensively explores the stability analysis of random nonlinear systems subjected to random non-instantaneous multiple impulses. The random non-instantaneous multiple impulses refer to various impulsive intensities, with the type of impulse at each moment determined by a Markov chain. Drawing on the properties of stochastic processes, a series of stability criteria are developed for the random non-instantaneous multiple impulsive systems within the constraint of fixed impulsive intervals. To validate the practicality of the proposed conceptual methods, the tracking control problem of network surface vessels under deception attacks is investigated, demonstrating feasibility through simulation results.