Stable controller design for mixed sensitivity reduction of infinite-dimensional systems

•We construct stable H∞H∞ controllers for infinite-dimensional systems.•Stable controllers achieve low sensitivity and robust stability simultaneously.•The plant we consider may have input/output delays and infinitely many zeros in C+C+.•The skew Toeplitz approach gives stable H∞H∞ controllers.

In this paper we study the design of stable controllers for mixed sensitivity reduction for systems that have input/output delays and infinitely many unstable zeros. The proposed method is based on interpolation with a unit in H∞H∞, which gives a necessary and sufficient condition for stabilization by stable controllers. Using the Youla parameterization, we introduce a two-block problem for the stable H∞H∞ controller design. The two-block problem is then transformed to a one-block problem solvable by the skew Toeplitz approach.