Approximate mixed synchronization by groups for a coupled system of wave equations

Article type: Research Article

Authors: Li, Tatsien^{a; *} | Rao, Bopeng^b

Affiliations: [a] Shanghai Key Laboratory for Contemporary Applied Mathematics; Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University, Shanghai 200433, China | [b] Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We first show that under a suitable balanced repartition of the mixed controls within the system, Kalman’s rank condition is still necessary and sufficient for the uniqueness of solution to the adjoint system associated with incomplete internal and boundary observations, therefore for the approximate controllability of the primary system by means of mixed controls. Then we study the stability of the approximately synchronizable state by groups with respect to applied controls.

Keywords: Mixed controls, stability of synchronizable state, wave equations

DOI: 10.3233/ASY-231865

Journal: Asymptotic Analysis, vol. 135, no. 3-4, pp. 545-579, 2023