This paper describes a stabilizing output feedback controller for a time-delay system that is derived from a complete quadratic Lyapunov-Krasovskii functional. Because the complete quadratic Lyapunov-Krasovskii functional contains non-constant coefficients for its decision variables, the stabilizing problem is more difficult to solve than the stability problem. Instead, this paper introduces a null term with a value of zero to convert the derivative of the Lyapunov-Krasovskii functional into a quadratic form and avoid the multiplication of decision variables. The controller design procedure is given by a stability condition based on the linear matrix inequality. The performance of the proposed controller is weighted to consider the dynamics of the controlled plant.
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