Inverse linear quadratic regulator of neutral time delay systems via finite dimensional Riccati equation

In this paper, a design method of an inverse LQ regulator of neutral time delay systems via finite dimensional Riccati equation is proposed. The existence of a solution of a finite dimensional Riccati equation is assumed, and the solution is calculated via Newton´s method, where the initial value is chosen with Homotopy method. The feedback law is constructed with it. It is shown that the resulting closed loop system is asymptotically stable, and moreover, it minimizes some quadratic cost functional. The design procedure is demonstrated with a numerical example.