Mixed sensitivity reduction for time-delay systems by stable controllers

This paper studies the mixed sensitivity problem within the framework of strong stabilization. We consider a class of time-delay systems having only a finite number of unstable poles. However the systems are allowed to possess pure delays and infinitely many unstable zeros. The new solution we propose here is rooted in an operator-theoretic approach to interpolation to address the infinite dimensionality. First we give a sufficient condition for sensitivity reduction by a stable controller. Next, using this condition, we introduce a two-block problem for the design of stable controllers achieving both low sensitivity and robust stability. Finally we transform the two-block problem to a one-block problem, which can be solved by matrix computations only. We also present numerical examples to illustrate the effectiveness of the proposed method.