Guaranteed LQR-Properties Control of Uncertain Linear Systems with Time-Delay of Retarded Type

Abstract

In the finite dimensional case, the linear quadratic regulator (LQR) is known to have good robustness properties. These properties are independent from choosing the weighting matrices in the cost functional. So, if a control system belongs to a class of LQRs, it is assured to have these robustness properties. In this paper, a method is proposed to construct a robust feedback controller for uncertain linear systems with time-delay of retarded type. The feature of this method is that the resulting closed loop system is assured to be an LQR for some cost functional. The cost functional contains some uncertainty, and it absorbs the uncertainty in the plant parameters so that a fixed feedback law is always optimal. The feedback gain is calculated with a solution of some linear matrix inequalities, and it is shown that the resulting closed loop system is an LQR for some cost functional, so it has the same robustness properties with the finite dimensional LQRs. Introducing an auxiliary system, it is possible to assign the degree of exponential stability of the closed loop system. A numerical example is given to demonstrate the effectiveness of this method.