Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization

We show that under Kalman’s rank condition, the observability of a scalar equation implies the uniqueness of solution to a system of elliptic operators. Using this result, we establish the asymptotic synchronization by groups for second order evolution systems

Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization

We show that under Kalman’s rank condition, the observability of a scalar equation implies the uniqueness of solution to a system of elliptic operators. Using this result, we establish the asymptotic synchronization by groups for second order evolution systems

Compensation spectrale et taux de décroissance optimal de l'énergie de systèmes partiellement amortis

We study the stabilization of systems of two equations in which only one equation is damped by a feedback control. We show that a well-chosen control can compensate for the real parts of the eigenvalues of the system and thus give the optimal polynomial energy decay rate of the system for smooth initial data

Uniqueness theorem for a coupled system of wave equations with incomplete internal observation and application to approximate controllability

We show that a Kalman rank condition is necessary and sufficient for the uniqueness of solution to a system of wave equations associated with incomplete internal observation without any restriction neither on the controlled subregion nor on the coupling matrices. The obtained result can be applied to the approximate internal controllability of the corresponding system