Guaranteed cost stabilization of neutral differential systems with parametric uncertainty

In this paper, we address the problem of the guaranteed cost stabilization for a class of neutral systems with parametric uncertainties and a given quadratic cost function. The parametric uncertainties are real time-varying norm bounded and state delay is a constant. The problem is to design the state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainty and delay. Two criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the Lyapunov method. The developed guaranteed cost controllers can be synthesized in terms of the feasible solutions to the certain matrix inequalities.