H∞ Control of Distributed and Discrete Delay Systems via Discretized Lyapunov Functional

Abstract

The discretized Lyapunov functional method is extended to linear systems with both, discrete and distributed delays, and to H∞ control. 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. In three numerical examples considered for retarded type systems, the resulting values of H∞-norm converge to the exact ones. The analysis results are applied to state-feedback H∞ 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. A numerical example illustrates the efficiency of the design method and the advantage of using distributed delay term in the feedback for H∞ control of systems with state delay.