MODEL-REDUCTION FOR CONTINUOUS-TIME AND DISCRETE-TIME-SYSTEMS VIA SQUARED-MAGNITUDE RESPONSES MATCHING BY LINEAR-PROGRAMMING

Abstract

The use of linear programming technique for the model reduction of continuous- and discrete-time systems is discussed. Based on squared-magnitude responses between the original system and its reduced model, a novel error function is presented. Two linear programming formulations are presented that use the L1-norm and the L infinity-norm of the proposed error function as respective criteria to solve the squared-magnitude problem. Finally, the reduced model is obtained by applying the factorization technique. Since the poles of the obtained squared-magnitude function are prevented from occurring on the j-omega axis (continous-time case) or unit circle (discrete-time case) by constraint, this approach ensures the stability of the reduced model. Some examples illustrate its applicability.