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A canonical reduced form for singular time invariant linear systems

M. Isabel Garcia-Planas
We consider quadruples of matrices $(E, A,B,C)$, representing
singular linear time invariant systems in the form \begin{equation}\label{c2eq1}\left .\begin{array}{rl}
E\dot x(t) &=
Ax+Bu\\ y&=Cx\end{array}\right \}\end{equation} with $E,A\in M_{p\times n}(C)$, $B\in M_{p\times
m}(C)$ and $C\in M_{q\times n}(C)$ under proportional and derivative
feedback and proportional and derivative output injection.

In this paper we present a canonical reduced form preserving the
structure of the system and provides a decomposition of the system into two independent
systems, one being a maximal regular system and the second one a minimal completely singular one.
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