Leader-following guaranteed-performance consensus design for singular multi-agent systems with Lipschitz nonlinear dynamics

Leader-following guaranteed-performance consensus problems for singular multi-agent systems with Lipschitz nonlinear dynamics are investigated. To obtain leader-following guaranteed-performance consensus, the consensus protocol and quadratic performance function based on state errors are proposed. Then, leader-following consensus problems of a nonlinear singular multi-agent system are transformed into asymptotic stabilization problems of a reduced-order subsystem by a new state decomposition method, and the impacts of the Lipschitz nonlinear dynamics are eliminated by using the structure property of the transformation matrix and the Lipschitz condition. Moreover, a guaranteed-performance consensualization criterion based on the Riccati inequality is given and the guaranteed-performance cost with a new structure is determined. Finally, a numerical simulation is shown to verify the validity of theoretical results.