Optimal closed-loop approximation by reduced order controllers

There are two different approaches to the problem of designing fixed, i.e. reduced, order controllers: the direct approach where a controller having a given order is sought, often as a solution of an optimization problem, and the indirect approach that consists of two steps. First, design of a controller that meets the desired specifications without order limitation and then approximating it by a low order one. In this paper, the authors present an accurate solution for the indirect approach which avoids the approximations (in the setting of the problem) that are commonly used. It is shown that after redefining the problem it is solved using the tools that were developed for direct optimization.