Decentralized Impulsive Control for Stochastic Systems Interconnected over Graphs*

This article is concerned with stability analysis and decentralized impulsive control problems for a class of interconnected stochastic systems (ISSs). The ISSs is a class of large scale systems with numbers of subunits interconnected over graphs and each subunit may subject to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${\it Ito}$</tex> -type noise disturbances. We first presented the related stability criteria for ISSs by using the stochastic multi-Lyapunov function. Secondly, an impulsive state feedback controller is designed to neutralize the stochastic disturbances and some instabilities caused by the interconnection among subsystems, at the same time the impulsive controller can guarantee that the closed-loop system have an ideal <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H_{\infty}$</tex> performance. At last, numerical simulations are established to prove the validity of the proposed methods.