Input-to-state stability for impulsive stochastic nonlinear systems with delayed impulses

Abstract

In this paper, the problems of the stochastic input-to-state stability (SISS) properties are investigated for impulsive stochastic nonlinear systems with delayed impulses. By employing Lyapunov method together with average impulsive interval approach, the sufficient conditions are established to ensure properties for impulsive stochastic systems with all stable subsystems. Moreover, the ISS properties are also derived for the stochastic systems when the system is with both stable and unstable subsystems. Then, we also study impulsive systems with multiple jumps, i.e. there exist different impulses in a system. By now, there has been no papers to consider multiple jumps for stochastic cases. Finally, two examples are provided to illustrate the effectiveness of our results.

Keywords:

• Impulsive system
• input-to-state stability
• delayed impulse
• unstable subsystems
• multiple jumps

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was jointly supported by the National Natural Science Foundation of China (61773217, 61374080, 11531006), the Scientic Research Fund of Hunan Provincial Education Department (18A013), and the Construct Program of the Key Discipline in Hunan Province.