Stability Verification of Nearly Periodic Impulsive Linear Systems using Reachability Analysis

Mohammad Al Khatib (1) , Antoine Girard (1) , Thao Dang (2)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 EDF R&D - EDF R&D

The paper provides stability analysis to certain classes of hybrid systems, more precisely impulsive linear systems. This analysis is conducted using the notion of reachable set. The main contribution in this work is the derivation of theoretical necessary and sufficient conditions for impulsive linear systems with nearly periodic resets subject to timing contracts. This characterization serves as the basis of a computational method for the stability verification of the considered class of systems. In addition, we show how this work handles the problem of timing contract synthesis for the considered class and we generalize our approach to verify stability of impulsive linear systems with stochastic reset instants. Applications on sampled-data control systems and comparisons with existing results are then discussed, showing the effectiveness of our approach.

Mots clés: Reachability; Impulsive systems; Stability analysis

Domaines: Systèmes et contrôle [cs.SY]; Automatique / Robotique; Optimisation et contrôle [math.OC]

Mohammad Al Khatib, Antoine Girard, Thao Dang. Stability Verification of Nearly Periodic Impulsive Linear Systems using Reachability Analysis. Analysis and Design of Hybrid Systems, IFAC, Oct 2015, Atlanta, United States. pp.358-363, ⟨10.1016/j.ifacol.2015.11.200⟩. ⟨hal-01276237⟩