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

Dan Ivanescu;  Silviu-Iulian Niculescu;  Jean-Michel Dion;  Luc Dugard — 2001

Kybernetika

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 γ -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 ∞ memoryless control problems in terms of Popov triplets...

On generalized Popov theory for delay systems

Silviu-Iulian Niculescu;  Vlad Ionescu;  Dan Ivanescu;  Luc Dugard;  Jean-Michel Dion — 2000

Kybernetika

This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoryless state feedback control law which guarantees the (exponential) closed-loop stability with an ℒ 2 norm bound constraint on disturbance attenuation. Note that the proposed results extend...

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