Unified Stability Criteria of Random Nonlinear Time-Varying Impulsive Switched Systems
Ticao Jiao, Wei Xing Zheng, Shengyuan Xu
Abstract
This paper investigates the problem of noise-to-state practical stability in mean (NSpS-M) (which is a natural generalization of noise-to-state stability in mean) and the problem of almost sure global asymptotic stability (GAS a.s.) for a class of random nonlinear time-varying impulsive switched systems. By using the notions of average impulsive switched interval and Poisson process, unified sufficient stability criteria on NSpS-M and GAS a.s. are derived. Two remarkable distinctions from the existing results lie in that: (1) stabilizing, inactive and destabilizing impulses are simultaneously considered; (2) the coefficient of the derivative of a Lyapunov function is allowed to be a time-varying function which can be both positive and negative and may even be unbounded. As an accompaniment, a less conservative unified criterion on NSpS-M for a special case is also presented by taking into account the stabilization role of the gain constant of the time-varying coefficient. Two examples are provided to illustrate the effectiveness of our derived criteria.