H∞ control of systems with distributed delay: Discretized Lyapunov functional method

Abstract

The discretized Lyapunov functional method is extended, for the first time, to H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control of linear neutral type systems with both, (single) discrete and distributed delays. The coefficients associated with the distributed delay are assumed to be piecewise-constant. A new Bounded Real Lemma (BRL) is derived in terms of Linear Matrix Inequalities (LMIs) via descriptor approach. The analysis results are applied to state-feedback H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control of linear neutral systems with discrete and distributed delays, where the controller may be either instantaneous or may contain discrete or distributed delay terms. In the numerical examples for retarded type systems, the resulting values of H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -norm generally converge to the exact ones. The new method essentially improves the existing H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control results. Moreover, it provides new tools for the important design problems, such as H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control of systems, which are not stabilizable without delay.