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

The discretized Lyapunov functional method is extended to linear systems with both, discrete and distributed delays, and to H1 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 H1-norm converge to the exact ones. The analysis results are applied to state-feedback H1 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 H1 control of systems with state delay.