Model reduction for the descriptor systems by linear matrix inequalities

摘要

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 H ₂ and H _∞ model reduction problems for the singular system using corresponding linear matrix inequalities. Especially frequency weighted H _∞ model reduction and mixed H ₂ and H _∞ model reduction are suggested as giving better frequency characteristics. The validity of the proposed method is shown by a numerical example.