PDEs with Distributed Control and Delay in the Loop: Transfer Function Poles, Exponential Modes and Robustness of Stability

摘要

In this paper we consider a large class of partial differential equations (PDEs) in one space dimen- sion with distributed control and with a time-delay in the feedback loop. We analyse the relationship between the poses of the closed-loop transfer func- tion and the exponential modes of the underlying retarded PDE in order to derive internal stability properties form external ones. Our approach is based on a combination of input-output methods and modal analysis.