Deterministic control of uncertain state delayed systems

Considers a robust stabilization problem in a state-space setting for a class of uncertain time-delay systems. The systems under consideration are described by a linear state-delayed equation whose matrices contain norm-bounded time-varying elements. Two novel designs of nonlinear controllers for coping with the uncertainties are presented. The first design is made possible by appropriately combining a state transformation technique with the second Lyapunov method. Specifically, the transformation technique is employed to convert the stabilization problem into an equivalent one which is solvable via the finite-dimensional Lyapunov min-max approach. The second design is mainly based on solving a certain infinite-dimensional Riccati equation arising in the optimal control theory for hereditary systems. The merits of the two designs are compared. An application of the main results to a certain model-following control problem is also demonstrated