Minimal Order Generalized State Space Representation of Singular Systems

In this paper, we consider the problem of obtaining minimal order generalized state space representations of systems described by equations of the form E¿(t) = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t) with E singular and det(sE - A)¿0. The underlying principle is that of removal of impulsive and exponential uncontrollable and unobservable modes. Based on this principle, a simple reduction procedure and a numerical algorithm are developed and illustrated by means of an example.