Delayed Feedback Control of Linear Systems with State Jump

Abstract

The effect of the delayed feedback control on the stability of periodic solutions of linear systems with sate jump is studied. Although the stability of the open-loop and the OGY feedback cases can be analyzed via matrix representations (Poincare map), the system with DFC requires an operator representation of the state transition on a certain function space due to the infinite-dimensionality caused by the time delay element in the controller. A stability condition is given in terms of the spectrum of this operator. Also an analytic formula and a numerical method for the computation of the spectrum are provided.