Robust stabilization of time delay systems based on riccati type operator equation arising in differential games

A robust stabilization problem is discussed for time delay systems. By introducing an indefinite Riccati type operator equation for time delay systems, we propose a design method of robust stabilizing control law against the parametric uncertainties, which occur in lumped parameter element and in all types of delay element. In the derivation of the control law, the key point is that we take a twofold approach; one is an internal approach based on Lyapunov type operator equation and another is an external approach based on small-gain theorem. This twofold approach first enable us to deal the uncertainties of time delay systems in a unified way.