Finite-time robust optimal passive control for a class of uncertain nonlinear systems

The finite-time passive control problem of a class of nonlinear uncertain systems with nonlinear terms satisfying Lipschitz conditions is studied. An optimal robust passive controller with respect to the finite-time interval is designed while noise inputs are energy bounded. Based on nonlinear passive control theory, the sufficient condition for the existence of finite-time robust passive controller such that the nonlinear uncertain control systems is finite-time boundedness for all admissible uncertainties and satisfies the given passive control index is given. By using the constructed Lyapunov function, applying linear matrix inequalities techniques and based on state feedback control, the design method of the finite-time optimal passive controller is derived. Simulation results demonstrate the validity of the proposed approach.