Guaranteed cost control for uncertain nonlinear systems with mixed time delays: The discrete time case
Abstract In this paper, the guaranteed cost control problem is investigated for a general class of discrete time uncertain nonlinear systems with mixed time delays. The mixed time delays under consideration comprise both the discrete and the distributed delays. By using the completing the square technique, the discrete and distributed time delays are handled in a unified framework. Then, by constructing an appropriate Lyapunov functional, a sufficient condition is established under which the closed loop control system is stable and an adequate performance index is guaranteed over all admissible uncertainties as well as mixed time delays. Based on the sufficient condition, the nonlinear cost guaranteed controller is designed and an explicit expression of the controller parameter is obtained. Finally, a numerical simulation example is presented to demonstrate the effectiveness and applicability of the results derived.
Eur. J. Control