Stochastic Input-to-State Stability of Impulsive Stochastic Nonlinear Systems in Infinite Dimensions
Pengfei Wang, Shuaiqi Wang, Huan Su
Abstract
This paper studies the stochastic input-to-state stability (SISS) of a class of impulsive stochastic nonlinear systems in Hilbert spaces. By constructing a class of proper Yosida strong solution approximating systems and using the infinite-dimensional version of Itô's formula, several novel Lyapunov-based sufficient criteria are given to ensure the SISS of mild solutions of the studied systems with destabilizing and stabilizing impulses, respectively. It should be pointed out that the SISS-Lyapunov function is nonexponential, which contains the exponential SISS-Lyapunov function as a special case. The average dwell time condition and the reverse average dwell time condition are respectively imposed to restrict the occurrence frequency of destabilizing and stabilizing impulses, which are more general than the fixed dwell time condition. As a subsequent result, the SISS of interconnected systems on networks is investigated by the Lyapunov method and the graph-theoretic technique. A new way of construction of the SISS-Lyapunov function for the entire interconnected systems on networks is provided by the SISS-vertex-Lyapunov functions and the interconnected topological structure. Finally, two examples are provided to show the effectiveness of the main results.