Stable feedback control of linear distributed parameter systems: Time and frequency domain conditions (Q1270926)

A controller for a distributed parameter system will normally be designed by using a finite-dimensional part of the original system. Hence the controller will work well for this finite-dimensional approximation. However, since one has ignored a part of the distributed parameter system, the controller is not a priori good for the original system. Connecting the controller to the original system may even lead to instability. The author presents for two types of stability, exponential and \(L^2\), sufficient conditions which guarantee that the connection of the controller with the distributed parameter system is stable.