Stabilization of LTI systems by relay feedback with perturbed measurements

Zohra Kader 1, 2, 3 Christophe Fiter 2, 1 Laurentiu Hetel 1, 2 Lotfi Belkoura 3, 1, 2
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 : This paper investigates the stabilization of Linear Time Invariant (LTI) systems by relay feedback. Generally the states measurements are subject to perturbations and noises. However, their effect is often ignored in the design of relay feedback. Here a state-dependent switching law is designed in a robust manner, while taking into account the perturbed states. The stability analysis of the closed loop system leads to qualitative conditions. Then, an LMI reformulation of the stability conditions is proposed to allow a numerical implementation of the results. Computer simulations show the efficiency of the developed method over a numerical example.
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Zohra Kader, Christophe Fiter, Laurentiu Hetel, Lotfi Belkoura. Stabilization of LTI systems by relay feedback with perturbed measurements. ACC 2016 - American Control Conference, Jul 2016, Boston, United States. pp.5169-5174, ⟨10.1109/ACC.2016.7526479⟩. ⟨hal-01415039⟩

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