Global optimization for the -norm model reduction problem

Abstract

A branch and bound algorithm is proposed to solve the -norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The -norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.

Acknowledgment

The authors wish to thank FAPESP and CNPq for providing financial support to this research work.