Uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems II: Case of Multiple Feedback Dampings

In this paper, the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dampings. They first show that under the observability of a scalar equation, Kalman’s rank condition is sufficient for the uniqueness of solution to a complex system of elliptic equations with mixed observations. The authors then establish a general theory on the asymptotic stability and the asymptotic synchronization for the corresponding evolutional system subjected to mixed dampings of various natures. Some classic models are presented to illustrate the field of applications of the abstract theory.