Observer-based stability controller for linear systems with delay in state

An observer-based stability controller is established for linear systems with delay in state. The controller not only realizes the separation of characteristic roots for the closed-loop system, but also makes the closed-loop transfer function equal to the transfer function of closed-loop constructed directly by state feedback. Using the separation of characteristic roots, the stability condition is presented. The controller can be obtained by solving two linear matrix inequalities (LMIs). Two illustrative examples are given to show the applicability of the proposed approach.