Model Reduction for the Descriptor Systems by Linear Matrix Inequalities

Model Reduction for the Descriptor Systems by Linear Matrix Inequalities

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.

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.