An Extension of a Lyapuov Approach to the Stabilization of Second Order Coupled Systems

Thierry Horsin (1) , Mohamed Ali Jendoubi (2)

1 M2N - Modélisation mathématique et numérique
2 UCAR - Université de Carthage (Tunisie)

This paper deals with the convergence to zero of the energy of the solutions of a second order linear coupled system. It revisits some previous results on the stabilization of such systems by exhibiting Lyapunov functions. The ones used are constructed according to some scalar cases situations. These simpler situations explicitely show that the assumptions made on the operators in the coupled systems seem, first, natural and, second, give insight on their forms.

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]

Thierry Horsin, Mohamed Ali Jendoubi. An Extension of a Lyapuov Approach to the Stabilization of Second Order Coupled Systems. ESAIM: Control, Optimisation and Calculus of Variations, 2020, 26, pp.19. ⟨10.1051/cocv/2019075⟩. ⟨hal-02941579v2⟩