Decentralized observer-based control of nonlinear interconnected systems with nonlinear dynamics

This paper presents a method for the design of decentralized state observer-based control for a class of systems which are modeled as nonlinear subsystems linked by nonlinear time varying interconnections. The non linearity of each subsystem satisfies the Lipschitz condition and the only information about the nonlinear interconnection is that satisfies a quadratic constraint. The key to our work is, in one hand, the reformulation of the Lipschitz condition and the quadratic constraint using the differential mean value to simplify the design of estimation and control matrices gains, and in another hand the use of the Lyapunov's direct method stability analysis. Sufficient conditions that ensure the existence of observer based feedback controller are established in terms of linear matrix inequalities. A numerical example is given to mark the effectiveness of the control design.