Reduction model approach for linear time-varying systems with input delays based on extensions of Floquet theory

Frédéric Mazenc 1, 2 Michael Malisoff 3
2 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
Abstract : We solve stabilization problems for linear time-varying systems under input delays. We show how changes of coordinates lead to systems with time invariant drifts, which are covered by the reduction model method and which lead to the problem of stabilizing a time-varying system without delay. For continuous time periodic systems, we can use Floquet theory to find the changes of coordinates. We also prove an analogue for discrete time systems, through a discrete time extension of Floquet theory.
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Frédéric Mazenc, Michael Malisoff. Reduction model approach for linear time-varying systems with input delays based on extensions of Floquet theory. Systems and Control Letters, Elsevier, 2016, 94 (August 2016), pp.70-76. ⟨10.1016/j.sysconle.2016.05.013⟩. ⟨hal-01389860⟩

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