A robust stability framework for LTI systems with time-varying sampling

Christophe Fiter 1, 2 Laurentiu Hetel 2, 1 Wilfrid Perruquetti 2, 3, 1 Jean-Pierre Richard 2, 3, 1
1 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
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
Abstract : This work aims at enlarging the sampling intervals in several state feedback control situations by designing a sampling map in the state space. We consider the case of linear time invariant (LTI) systems with state-bounded perturbations, and guarantee their exponential stability for a chosen decay-rate. The approach is based on linear matrix inequalities (LMIs) obtained thanks to Lyapunov-Razumikhin stability conditions and convexification arguments. First, it enables to optimize the lower-bound of the sampling maps by computing the adequate Lyapunov-Razumikhin function. This result can be interpreted as a robust stability analysis with respect to arbitrary time-varying sampling intervals, which may be useful in the case of uncontrolled sampling, or in the presence of phenomenon such as sampling jitter. Then, the obtained results are extended to design the sampling map in three dynamic sampling control situations: event-triggered control, self-triggered control, and state-dependent sampling. The results are illustrated with a numerical example from the literature.
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Christophe Fiter, Laurentiu Hetel, Wilfrid Perruquetti, Jean-Pierre Richard. A robust stability framework for LTI systems with time-varying sampling. Automatica, Elsevier, 2015, 54, pp.56-64. ⟨10.1016/j.automatica.2015.01.035⟩. ⟨hal-01194561⟩

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