Guaranteed Cost Consensus for Fuzzy Multi-Agent Systems With Switching Topologies

This paper concentrates on guaranteed cost consensus problem for nonlinear multi-agent systems (MASs) under directed switching topologies. First, a novel polynomial fuzzy model is constructed for describing the nonlinear error MASs that are formulated by follower agents and a leader agent. Then, a consensus tracking protocol is devised to ensure that the MASs with changing topologies can achieve agreement. For the established fuzzy MASs, guaranteed cost function is introduced based on error states and control inputs. By the multiple polynomial Lyapunov function, we present relaxed sufficient condition to reach consensus with a guaranteed cost for the fuzzy MASs. Moreover, the designed consensus protocol can realize guaranteed cost by the upper bound for any initial error state. The obtained condition is converted to sum of squares and solved numerically. Finally, an example is given to illustrate the validity of the proposed consensus technique.