A design method for a linear quadratic regulator for systems with time-delay to locate all poles in the specified half plane.

In this paper, a method to construct a linear state feedback law for systems with time-delay is proposed. This method yields a state feedback law by which all poles of the closed loop system are located in the specified half plane. The feedback gain is given from a solution of an infinite dimensional Riccati equation for an auxiliary system defined for the plant. The closed loop system composed by this method is a linear quadratic regulator for a certain criterion. This means that the closed loop system satisfies the circle condition, and thus it has a good robustness property. Moreover, the closed loop system is assured to have an exponential stability with the assigned degree of stability. The proposed design method is quite efficient because an infinite number of poles of the system with time delay can be placed in the desired region by choosing a small number of design parameters.