Robust H∞ control of linear time-varying systems with mixed delays in the Hilbert space

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.