Observer design and stability analysis for a class of PDE chaotic systems

摘要

This paper deals with observer design and stability for a class of partial differential equation (PDE) systems governed by one-dimensional wave equations with mixed derivative terms and superlinear boundary conditions, whose dynamics exhibits chaos when the system parameters change within certain ranges. Firstly, a sufficient and necessary condition that guarantees the stability of this class of systems is obtained. Secondly, based on the method of characteristics, an observer is designed by injecting the measurement output estimation error on the boundary, and the observation error dynamics is proved to be stable with a necessary and sufficient criterion, which can identity the range of the feedback gain for the observer. Finally, two numerical examples are provided to illustrate the validity of the theoretical conclusions. @@@ ? 2021 The Franklin Institute. Published by Elsevier Ltd.

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