Equivalence and Solutions of Descriptor Linear Systems

Modeling is probably the most basic topic in any system theory. In Sect. 1.1, we introduced the state space representation of descriptor systems which depends very much on the state vector selected. Since there exist different choices of the state vector variables, the state space representation of a given descriptor system is certainly not unique. In normal linear systems theory, this phenomenon has been well described by the concept of algebraic equivalence (see Duan 1996a, 2004a). The purpose of this chapter is to generalize this concept into the case of descriptor linear systems, and based on which to examine some of the basic equivalent structures and the solution of a general descriptor linear system.