1. A robust stability framework for LTI systems with time-varying sampling
- Author
-
Christophe Fiter, Laurentiu Hetel, Jean-Pierre Richard, Wilfrid Perruquetti, Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Non-Asymptotic estimation for online systems (NON-A), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Région Nord - Pas de Calais project ARCIR ESTIREZ, ANR-14-CE27-0008,ROCC-SYS,Commande Robuste des Systèmes Cyber-Physiques(2014), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
- Subjects
Linear matrix inequality ,Sampling (statistics) ,state-dependent sampling ,Stability (probability) ,event-triggered control ,LTI system theory ,Stability conditions ,self-triggered control ,sampled-data control ,sampling jitter ,Exponential stability ,time-varying sampling ,Control and Systems Engineering ,Control theory ,[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering ,Lyapunov-Razumikhin ,State space ,Electrical and Electronic Engineering ,linear matrix inequality ,Importance sampling ,convex embedding ,Mathematics - Abstract
International audience; 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.
- Published
- 2015
- Full Text
- View/download PDF