A Robust Polytopic Approach for State-Dependent Sampling

Christophe Fiter 1, * Laurentiu Hetel 1 Wilfrid Perruquetti 1, 2, 3 Jean-Pierre Richard 1, 2, 3
* Corresponding author
1 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
2 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 : This work aims at decreasing the number of sampling instants in state feedback control for perturbed linear time invariant systems. The approach is based on linear matrix inequalities obtained thanks to Lyapunov-Razumikhin stability conditions and convexification arguments that guarantee the exponential stability for a chosen decay-rate. First, the method enables to perform a robust stability analysis regarding time-varying sampling and to maximize a lower-bound estimate of the maximal allowable sampling interval, by computing the adequate Lyapunov-Razumikhin function. Then, it makes it possible to design a state-dependent sampling control scheme that enlarges even further the maximal allowable sampling intervals.
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Christophe Fiter, Laurentiu Hetel, Wilfrid Perruquetti, Jean-Pierre Richard. A Robust Polytopic Approach for State-Dependent Sampling. ECC 2013 : 12th European Control Conference, Jul 2013, Zurich, Switzerland. pp.2603 - 2608. ⟨hal-00849833⟩

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