A Self-Triggered Control Based on Convex Embeddings for Perturbed LTI Systems

Christophe Fiter 1, * Laurentiu Hetel 2 Wilfrid Perruquetti 2, 3, 4 Jean-Pierre Richard 2, 3, 4
* Corresponding author
2 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
3 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this work, we present a novel self-triggered control which aims at decreasing the number of sampling instants for the state feedback control of perturbed linear time invariant systems. The approach is based on convex embeddings that allow for designing a state-dependent sampling function guaranteeing the system's exponential stability for a desired decay-rate and norm-bounded perturbations. One of the main contributions of this paper is an LMI based algorithm that optimizes the choice of the Lyapunov function so as to enlarge the lower-bound of the sampling function while taking into account both the perturbations and the decay-rate. The advantages of the approach are illustrated with a numerical example from the literature.
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Christophe Fiter, Laurentiu Hetel, Wilfrid Perruquetti, Jean-Pierre Richard. A Self-Triggered Control Based on Convex Embeddings for Perturbed LTI Systems. 9th IFAC Symposium on Nonlinear Control Systems, Sep 2013, Toulouse, France. pp.335-340, ⟨10.3182/20130904-3-FR-2041.00176⟩. ⟨hal-00849840⟩

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