Stability and consensus for T-S fuzzy complex dynamical networks

This paper investigates the H
_∞
stability and consensus of discrete-time nonlinear complex dynamical network systems based on T-S fuzzy model. The nonlinear complex dynamical network system consists of N discrete-time T-S fuzzy subsystems. Parallel distributed compensation algorithm and Lyapunov method are applied to design an H
_∞
decentralized fuzzy controller. By considering the characteristic of interconnection matrix of the network, the test of the stability of a network 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.