H<inf>∞</inf>-guaranteed cost control for linear systems with time-delay

Abstract

Solving state feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> control problem usually leads to controller gain too large. A effective method to solve the problem is simultaneously to introduce guaranteed cost control. The delay-dependent H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> -guaranteed cost control problem for linear systems with state delay is investigated. A delay-dependent condition for the existence of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> and guaranteed cost memoryless state feedback controller is presented in terms of matrix inequality such that the resulting closed-loop system is asymptotically stable and guarantees H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance index, and an upper bound on the given cost function can be obtained. Furthermore, a design method of the optimal H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> -guaranteed cost controller is given against the constant initial value. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed results.