Design of Observer-Based Controllers for Lipschitz Nonlinear Systems by Using LMIs

This paper deals with the observer-based output feedback control for a class of nonlinear systems with Lipschitz nonlinearities and affected by noises. Stability in the absence of disturbances and input-to-state stability in the presence of disturbances are established under suitable conditions that are given by bilinear matrix inequalities. Since there are no general tools to solve such inequalities, gridding and linear matrix inequalities will be used. A design method is presented to find solutions satisfying such conditions. Numerical tests are reported to illustrate the effectiveness of the resulting regulator as compared to other approaches based on linearized models of the plant.