Robust stabilization of uncertain time delay systems via combined internal-external approach

A robust stabilization problem is discussed for time delay systems. By introducing an indefinite Riccati-type operator equation for time delay systems, a design method for a stabilizing control law robust against parametric uncertainties, which occur in lumped-parameter elements and in all types of delay element, is obtained. In the derivation of the control law, a combined approach is taken: an internal approach based on a Lyapunov-type operator equation is combined with an external approach based on the small-gain theorem. This enables the uncertainties of time delay systems to be dealt with in a unified way