Robust guaranteed cost H∞ control for uncertain time-varying delay system

Abstract

This paper studies the problem of robust H∞ guaranteed cost control for a class of time-varying uncertain continuous systems with both state and input delays. Suppose that the time-varying uncertain parameters are norm-bounded, but the matched conditions are not required to satisfy. A new sufficient condition of H∞ robust stabilization which satisfies guaranteed cost index is given for the systems by constructing the generalized Lyapunov function and taking the linear matrix inequality approach. Robust H∞ guaranteed cost controllers can be realized simply by solving the corresponding linear matrix inequalities so that a guaranteed cost function for the closed-loop systems has an upper bound irrespective of all admissible parameter uncertainties. Then, by iterative approach, the optimal robust H∞ guaranteed cost controllers can be obtained through the corresponding convex optimization. A numerical example is given to show the potential of the proposed technique.