Static output feedback control for H∞ stability and consensus of nonlinear complex dynamical networks

This paper investigates the H_∞ stability and consensus of uncertain discrete-time nonlinear complex dynamical network systems based on T-S fuzzy model. The nonlinear complex dynamical network system consists of N nonlinear discrete-time subsystems. Parallel distributed compensation algorithm and Lyapunov method are applied to design an H_∞ decentralized fuzzy static output feedback controller. Based on Lyapunov method, a static output feedback controller is designed to guarantee that the closed-loop system is asymptotically H_∞ stable. By considering the characteristic of interconnection matrix of the network, the test of the stability of the network system is separated in to the test of the stability of the several nonlinear systems. Furthermore, the consensus problem for the leader-follower complex dynamical network is considered. And the proposed criterion can be obtained by solving a set of linear matrix inequalities (LMIs) which are numerically feasible. The effectiveness of the proposed methods is demonstrated through numerical examples.