Optimal H∞ Guaranteed Cost Controller for Uncertain Time-Delay Linear Systems

The purpose of this paper is to design a robust Hinfinity controller for uncertain time-delay linear systems so that reduces the conservatism and guarantees cost control. A delay-dependent condition is presented for the essence of Hinfinity guaranteed cost state feedback controller in terms of matrix inequality (MI) so that ensures asymptotic stability of uncertain time-delay linear system with state feedback. This condition guarantees essence an upper limit for given cost control and H-infinity performance index. Then the mentioned condition is transformed to the solvability of a linear matrix inequality (LMI) by using Schur complement. A design method of the optimal H-infinity guaranteed cost controller is obtained by a constant initial value and convex optimization method which is solved by LMI Toolbox in Matlab. In addition to, it is applied a condition in the cost function which would not reduce the generality of the problem and caused a result with less conservatism. Finally, the feasibility, the effectiveness and the less conservatism of this method is demonstrated by a numerical example.