Fundamental properties of the manifold of singular and regular linear systems (Q1087849)

This paper constructs a real analytic manifold L of equivalence classes of systems of the form \(Ex'=Ax+Bu\), \(y=Cx\). Here E, A, B, C are constant matrices, E, A are square, and the pencil zE-A is regular. It is shown that L is the completion, with respect to solutions of the set of regular state space systems, that is those with E nonsingular. Other geometric and analytic properties of L are established, including genericity of the regular systems.