Solutions to the combined sensitivity and complementary sensitivity problem in control systems

In a recent paper, a set of necessary and sufficient conditions for the existence of solutions to the combined sensitivity and complementary sensitivity (CSCS) problem in control systems was given. However, a practical method for constructing solutions to this problem was not presented. The computation procedure that was proposed involves constructing a sequence of rational functions to approximate an irrational function and may result in complicated high-order controllers. In this paper, we consider the synthesis aspect of the CSCS problem and derive an algorithm for constructing controllers that solve our CSCS problem in a simple manner. Moreover, an error in the closed-form solution of the Nevanlinna-Pick interpolation problem is revealed.