Abstract
The problems of robust stabilization and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control for uncertain discrete-time systems with time-varying delays are investigated. Attention is focused on the design of a memoryless H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state feedback controller such that the resulting closed-loop system is robustly exponentially stable with a prescribed level for all admissible uncertainties. A new delay-dependent sufficient condition for the existence of robust exponential H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> state feedback controllers is provided by constructing a new Lyapunov functional and introducing some slack matrix variables. The desired H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller can be obtained by solving a set of matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.
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