A generalized linear-quadratic optimal control problem for systems with delay is formulated. The optimal solution is given as a state feedback form which requires a solution of coupled infinite-dimensional Riccati equations. It is shown that the closed-loop system formed by the optimal state feedback control has some desirable sensitivity and robustness properties. The generalization exists in the state quadratic form of the cost functional, which makes it possible to discuss a pole location problem within the framework of the linear-quadratic optimal control problem. It is also shown that the generalized cost functional contains a special class of cost functionals for which the optimal control can be realized by solving only a finite-dimensional Riccati equation. Based on these results about the generalized linear-quadratic optimal control, a design method of feedback controls is proposed and an illustrative example is then presented.
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