Guaranteed Cost Control of Polynomial Nonlinear Uncertain Systems with Time-Delay

This paper focuses on the problem of guaranteed cost control of polynomial nonlinear uncertain systems with time-delay. Both the state and control uncertainties, which are unknown but bounded by some continuous nonlinear functions, are taken into consideration. Based on the tenets of sate-dependent polynomial Lyapunov functions, we developed a state feedback controller to obtain an upper bound for the guaranteed and optimal cost by using the Sum of Squares technique. Finally, numerical results were presented to demonstrate the effectiveness of the proposed approach.