Controller Reduction with Consideration of Closed-Loop Performance and Stability.

Abstract

In this paper we consider controller reduction preserving both performance and stability of the closed-loop system. First, a quadratic cost is introduced which represents the performance of the closed-loop system formed by a linear multivariable plant and high-dimensional dynamic controller. Then the controller reduction problem is formulated as the problem of finding a fixed low-dimensional dynamic controller preserving stability and value of the quadratic cost. Secondly, by using the Lyapunov equation, the problem is converted into the convex optimization problem with constraint described by a linear matrix inequality (LMI), and the sufficient condition for the existence of such an optimal reduced controller is shown. Finally, an example illustrates the methodology.