Matrix norm approach for control of linear time-delay systems

André R. Fioravanti 1, 2 Catherine Bonnet 1, 2 Silviu-Iulian Niculescu 2 José Claudio Geromel 3
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
2 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : The aim of this paper is to present some results on the control synthesis of time-delay linear systems. Our objective is to find linear controllers able to increase the first stability window imposing that the delay-free system is stable. Our method treats time-delay systems control design with numeric routines based on Linear Matrix Inequalities (LMI) arisen from classical linear time invariant system theory coupled together with a unidimensional search. The proposed algorithm is simple, efficient and easy to be numerically implemented. Some examples illustrating state and output feedback design are solved and discussed in order to shed the light on the most relevant characteristic of the theoretical results. The paper ends with some discussion on further theoretical extensions of the proposed methodology.
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André R. Fioravanti, Catherine Bonnet, Silviu-Iulian Niculescu, José Claudio Geromel. Matrix norm approach for control of linear time-delay systems. CDC-ECC 2011 : 50th IEEE Conference on Decision and Control and European Control Conference, Dec 2011, Orlando, United States. pp.4170-4175, ⟨10.1109/CDC.2011.6161359⟩. ⟨hal-00664506⟩



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