Event-Triggered Stabilizing Controllers for Switched Linear Systems

Fairouz Zobiri 1, 2 Nacim Meslem 2 Brigitte Bidégaray-Fesquet 1
1 EDP - Equations aux Dérivées Partielles
LJK - Laboratoire Jean Kuntzmann
2 GIPSA-SYSCO - SYSCO
GIPSA-DA - Département Automatique
Abstract : We introduce an event-triggered algorithm for the stabilization of switched linear systems. We define a pseudo-Lyapunov function common to all the subsystems. The pseudo-Lyapunov function is compared, at every time instant , to an exponentially decreasing upper threshold. An event is generated when the two functions intersect, or when a new subsystem becomes active. The existence of a Lyapunov function common to all the subsystems is a key requirement of this method. Nevertheless, imposing this condition does not add to the complexity of the problem. Indeed, we formulate the problem in terms of Linear Matrix Inequalities, as a generalized eigenvalue problem. This formulation allows to simultaneously check for the existence of a common Lyapunov function and to obtain the optimal parameters to define the upper threshold. We prove the stability of the system under the event-triggered control and we show that successive events are separated by a minimum interval of time.
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Fairouz Zobiri, Nacim Meslem, Brigitte Bidégaray-Fesquet. Event-Triggered Stabilizing Controllers for Switched Linear Systems. Nonlinear Analysis: Hybrid Systems, Elsevier, 2020, 36, pp.100831. ⟨10.1016/j.nahs.2019.100831⟩. ⟨hal-02171814⟩

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