Event-triggered stabilizing controllers for switched linear systems. (May 2020)

• Record Type: Journal Article
• Authors: Zobiri, Fairouz; Meslem, Nacim; Bidegaray-Fesquet, Brigitte
• Is Part Of: Nonlinear analysis. Volume 36(2020)
• Publication Date: 2020-05
• Subjects: Event-triggered control -- Switched linear system; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2019.100831
• Languages: English
• ISSNs: 1751-570X

Abstract

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. Highlights: Application of event-triggered control to switched linear systems. Simple method that requires few design parameters. An optimization method is proposed to tune the parameters.