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Model Reduction for the Descriptor Systems by Linear Matrix Inequalities

Do-Chang Oh and Eun-Tae Jeung
International Journal of Control, Automation, and Systems, vol. 8, no. 4, pp.875-881, 2010

Abstract : In this paper we propose the singular structure preserving model reduction for SISO(single-input/single-output) descriptor systems. A continuous-time descriptor system is decomposed into the slow system and the fast system, and then the fast system is projected into a discrete-time system with controllability and observability matrices the same as those of the original fast system. As a result, we found the respective solutions of H2 and H∞ model reduction problems for the singular system using corresponding linear matrix inequalities. Especially frequency weighted H∞ model reduction and mixed H2 and H∞ model reduction are suggested as giving better frequency characteristics. The validity of the proposed method is shown by a numerical example.

Keyword : Descriptor system, fast system, H2 and H∞ model reduction, linear matrix inequality, mixed H2 and H∞ model reduction, weighted model reduction.

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