On the optimal control of time delay systems: a complete type functionals approach

In this contribution, we revisit some aspects of the optimal control problem for time delay systems in the light of the recent contributions on the construction of Lyapunov Krasovskii functionals of complete type. For any stable linear time delay system, the existence of these functionals is insured and they can be easily constructed. Furthermore, they admit a quadratic lower bound. Thanks to these features, we are able to give some new insight into the guaranteed cost control problem and to present a performance index for which the optimality of the control law is fully established. An illustrative example is discussed.