A global optimization approach for the problem of controller order reduction

Abstract

A novel formulation for the problem of optimal controller order reduction for continuous-time linear systems is presented. The H2 or the H∞-norms of the error realization between the full and the reduced order controlled systems are used as optimization criteria. Linear matrix inequality optimization problems provide the upper and the lower bounds required for the branch and bound algorithm used to solve the order reduction problem. The convergence in finite time to the global optimum is assured. An example illustrates the results.