Discrete and intersample analysis of systems with aperiodic sampling

Laurentiu Hetel 1, * Alexandre Kruszewski 2 Wilfrid Perruquetti 2, 3 Jean-Pierre Richard 3, 1
* Corresponding author
1 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
3 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
Abstract : This article addresses the stability analysis of linear time invariant systems with aperiodic sampled-data control. Adopting a difference inclusion formalism, we show that necessary and sufficient stability conditions are given by the existence of discrete-time quasi-quadratic Lyapunov functions. A constructive method for computing such functions is provided from the approximation of the necessary and sufficient conditions. In practice, this leads to sufficient stability criteria under LMI form. The inter-sampling behavior is discussed there: based on differential inclusions, we provide continuous-time methods that use the advantages of the discrete-time approach. The results are illustrated by numerical examples that indicate the improvement with regard to the existing literature.
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Laurentiu Hetel, Alexandre Kruszewski, Wilfrid Perruquetti, Jean-Pierre Richard. Discrete and intersample analysis of systems with aperiodic sampling. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2011, 56 (7), pp.1. ⟨10.1109/TAC.2011.2122690⟩. ⟨hal-00576366⟩

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