Guaranteed Cost Control for a Class of Discrete-Time Systems with Saturation Nonlinearities

Abstract

For a class of discrete-time systems with saturation nonlinearities, the design problem of the optimal guaranteed cost state feedback controller is formulated in this paper. Together with a given quadratic cost index, a sufficient condition for the existence of state feedback guaranteed cost controller is derived by the means of Lyapunov stability theory and linear matrix inequalities(LMI). Furthermore, a LMI based new criterion that the optimal guaranteed cost control problem of state feedback control law is proposed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.