Abstract

In this paper, a class of linear infinite‐dimensional systems with discrete and distributed time‐varying delays is studied. New sufficient conditions for the robust H ∞ control of linear time‐varying control systems with mixed time‐varying delays in Hilbert spaces have been established. The conditions are given in terms of the solution of a Riccati differential equation. Furthermore, it is proved for the first time that the solution to the robust H ∞ control problem can be solved by the global controllability of an appropriate linear control delay‐like system. Copyright © 2010 John Wiley & Sons, Ltd.