Containment Control for Fuzzy Multi-Agent Systems Subject to Stochastic Controller Gain Variation

Abstract

This paper studies the containment control problem for a kind of nonlinear discrete-time multi-agent systems (MASs)with stochastic controller gain variation. More specifically, the nonlinear dynamics of MASs are modeled by the discrete-time Takagi-Sugeno (T-S)fuzzy systems, which can approximate many practical nonlinear systems in reality. Firstly, by introducing a stochastic variable and an uncertain term in the control protocol, a stochastic uncertain closed-loop system is derived that captures the stochastic controller gain variation phenomenon. By means of the Lyapunov stability theory and linear matrix inequality (LMI)technique, a novel sufficient condition is obtained such that containment control for such a kind of nonlinear systems is achieved. Then, after some matrices manipulation, the controller gains are calculated by solving some LMIs. A numerical study is finally proposed for the validation of the controller design.