UNIQUENESS OF SOLUTION TO SYSTEMS OF ELLIPTIC OPERATORS AND APPLICATION TO ASYMPTOTIC SYNCHRONIZATION OF LINEAR DISSIPATIVE SYSTEMS

摘要

We show that under Kalman's rank condition on the coupling matrices, the uniqueness of solution to a complex system of elliptic operators can be reduced to the observability of a scalar problem. Based on this result, we establish the asymptotic stability and the asymptotic synchronization for a large class of linear dissipative systems.