Stabilization of linear distributed systems under switching control constraint

Département de Mathématiques, Ecole Normale Supérieure de Rabat, BP 5118, Morocco

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Received: 31 January 2025
Accepted: 9 March 2026

Abstract

We consider a class of infinite-dimensional linear control systems with controls subject to possible saturation. The aim is to study the stabilization under the additional switching control constraint which means that only one actuator is active. The appropriate feedback turns out to be multivalued and the existence of the solution to the resulting differential inclusion is established by using nonlinear semigroup theory. The switching control property occurs whenever the set of instants at which the trajectory intersects some specified subsets of the state space is of null measure. In the multivalued feedback framework, asymptotic stability and asymptotic output stability are obtained from LaSalle invariance principle. We establish also other stabilization results by constructing suitable state dependent switched systems where only one control is activated in each subsystem. Applications to the simultaneous stabilization under switching control constraint are treated for various partial differential equations. The latter includes heat, plate and wave systems.