Noise-to-state stability criteria of switching stochastic nonlinear systems with synchronous and asynchronous impulses and its application to singular systems

In this paper, the problem of noise-to-state stability of switching stochastic nonlinear systems with synchronous and asynchronous impulses is addressed. Compared with the existing results, the phenomenon of synchronous and asynchronous impulses is taken into account at the same time. Then, synchronous and asynchronous impulsive sequences are properly constrained in terms of eventually uniform boundedness, which are substantially broader than the previously defined impulsive signals. In addition, multiple Lyapunov functions with the time-varying infinitesimal operator are employed to derive some noise-to-state stability criteria. Furthermore, the obtained result is applied to a general class of singular systems, where inherent state jumps raised by switching behavior and abrupt state changes induced by external factors are considered simultaneously, and some computable stability conditions are given.