Stochastic finite-time stability and stabilization for stochastic nonlinear systems with impulse effects

Abstract

In this paper, some unified stochastic finite-time stability (SFTS) criteria are derived for the impulsive stochastic nonlinear systems by using the stochastic analysis theory, stopping time technology, Lyapunov approach and limit average dwell time (LADT) technology when the impulse effect is destabilizing impulse or stabilizing impulse. Meanwhile, in order to achieve stochastic finite-time stabilization for stochastic nonlinear systems, the impulse control approach is also obtained, which can be divided into two cases: (1) A stochastic finite-time instable (SFTI) stochastic system can become SFTS under the impulse control strategy; (2) A SFTS stochastic system can keep the SFTS under the impulsive disturbance. Furthermore, by using the impulse dependent average dwell time (IDADT) technology, the results are also established for the multiple impulse effects, i.e. destabilizing impulse and stabilizing impulse exist in the system simultaneously. Finally, two useful examples are provided.