Kybernetika 37 no. 3, 325-343, 2001

Control of distributed delay systems with uncertainties: a generalized Popov theory approach

Dan Ivanescu, Silviu-Iulian Niculescu, Jean-Michel Dion and Luc Dugard

Abstract:

The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for $\gamma$-attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov-Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of $H^\infty$ memoryless control problems in terms of Popov triplets and associated objects. The approach is illustrated via numerical examples.