Lyapunov Matrix-Based Method to Guaranteed Cost Control for A Class of Delayed Continuous-Time Nonlinear Systems

This article involves the problems of stabilization and guaranteed cost control for a class of delayed continuous-time nonlinear systems. The sufficient conditions for the existence of stabilization controllers and guaranteed cost controllers are investigated by constructing a new Lyapunov matrix-based Lyapunov–Krasovskii functional. These conditions can be easily verified by using standard compute software (e.g., the toolbox YALMIP of MATLAB), since they are expressed as simple linear matrix inequalities. Furthermore, the feasible solutions of these linear matrix inequalities are used to describe the explicit forms of stabilization controllers and guaranteed cost controllers. Finally, the validity of the proposed Lyapunov matrix-based LKF method is tested by two numerical examples.