A Note on Order and Index Reduction for Descriptor Systems

• 成果类型: Article
• 署名作者: Corless, Martin J.; Shorten, Robert N.
• 署名单位: Purdue University System; Purdue University; Imperial College London; University College Dublin
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3121207
• 发表日期: 2022
• 页码: 4293-4299
• 关键词: standards; indexes; Matrix decomposition; dynamical systems; switches; reduced order systems; mathematical models; descriptor systems; quasi-Weierstrass form; system order reduction

摘要

We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection between classical and new results on this topic, and lead to an elementary construction of quasi-Weierstrass forms for a descriptor system. Examples are given to illustrate the usefulness of our results.