In this paper, a method to design an inverse LQR with a retarded state predictor for systems with time-delay in state and input is proposed. A feedback law is constructed by using the predictor which has a same state time-delay as the one in the systems. It is shown that the resulting closed-loop system is asymptotically stable and the proposed feedback law is an optimal control that minimizes a quadratic cost functional. Furthermore, we show that the constructed regulator has good robustness as same as an ordinary finite-dimensional LQR. Finally, numerical examples are given to evaluate the effectivity of the proposed method.
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