Polytopic Discrete-Time Models for Systems with Time-Varying Delays

Warody Lombardi 1 Silviu-Iulian Niculescu 2, 3 Sorin Olaru 2, 1
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
3 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : This paper focuses on the modeling of linear systems with time-varying input delays. During the discretization process, three cases can be differentiated with respect to the structure of the continuous-state transition matrix: non-defective with real eigenvalues, non-defective with complex-conjugated eigenvalues and defective matrices with real/complex-conjugated eigenvalues. The goal is to model the variable input delays as a polytopic uncertainty in order to preserve a linear difference inclusion framework. It is shown that the embedding problem can be translated into a polytopic containment problem and an iterative approach to the construction of tight, low complexity embedding (in terms of a simplex body) is proposed.
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Submitted on : Monday, November 12, 2012 - 4:16:39 PM
Last modification on : Tuesday, June 4, 2019 - 11:08:06 AM

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Warody Lombardi, Silviu-Iulian Niculescu, Sorin Olaru. Polytopic Discrete-Time Models for Systems with Time-Varying Delays. Time Delay Systems: Methods, Applications and New Trends, Springer, pp.277-288, 2012, Lecture Notes in Control and Information Sciences. Volume 423, ⟨10.1007/978-3-642-25221-1_21⟩. ⟨hal-00750895⟩

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