Structural decomposition of general singular linear systems and its applications

Abstract

Singular systems can be found in many real life problems, such as economic systems, biological systems, engineering systems and social systems, to name a few. In this thesis, we aim to exploit the philosophy and development of a powerful structural decomposition technique, which is capable of explicitly capturing the structure properties of singular linear systems. Such a technique, like its counterpart for nonsingular systems, is expected to play an important role in solving many systems and control problems related to singular systems. The main contributions of the thesis are: 1) the development of a structural decomposition of general multivariable singular systems; 2) the detailed connections and proofs of the structural properties of singular systems including geometric subspaces in the framework of the structural decomposition; and 3) applications of the proposed technique to some control problems related to singular systems. All these aspects are thoroughly studied in the thesis. Some preliminary application results show that the structural decomposition technique is indeed a powerful tool.