Partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls

Abstract

In this paper, we propose the concept of partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls, and make a deep discussion on it. We analyze the relation-ship between the partial approximate boundary synchronization and the partial exact boundary synchronization, and obtain sufficient conditions to realize the partial approximate boundary synchronization and necessary conditions of Kalman's criterion. In addition, with the help of partial synchronization decomposition, a condition that the approximately synchronizable state does not depend on the sequence of boundary controls is also given.

Keywords

Coupled system of wave equations / partial approximate boundary synchronization / partially approximately synchronizable state

References

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2020 Higher Education Press