Robust stabilization of uncertain time delay systems via internal and external approaches

The authors solve a robust stabilization problem defined for time delay systems. They take a twofold approach to the derivation of the robust stabilizing control law: the internal approach based on a Lyapunov type operator equation and the external approach based on the small-gain theorem. The internal approach enables one to solve a restricted robust stabilization problem by introducing an indefinite Riccati type operator equation. Then, as the internal approach is not applicable for the analysis of the point delay element, the external approach is used to analyze the robust stability against the uncertainty of the point delay element. Finally, by exploiting the merits of both approaches, a robust stabilizing control law against all types of the perturbations is obtained