Robust stability, adjoints and LQ control of scale delay systems

The Lyapunov-Krasovskii theory is used to derive sufficient conditions for robust stability (independent of delay) for a special class of functional differential systems with time variant delays. The existence of a triple of positive definite matrices satisfying a certain Riccati-like equation is shown to imply the robust stability. The connection between Hurwitz stability and Schur-Cohn stability of certain system matrices with this Riccati equation is presented. The approach readily yields stabilizability conditions under state feedback. The adjoint equations and optimal LQ control for such systems are derived. It is shown that the optimal regulator involves the feedback of a formal series of point delayed states. A sufficient condition for convergence of this series is given.