Functional Output-Controllability of Time-Invariant Singular Linear Systems

Abstract

In the space of finite-dimensional singular linear continuous-time-invariant systems described in the form

$$\displaystyle{ \left.\begin{array}{rl} E\dot{x}(t)& = \mathit{Ax}(t) + \mathit{Bu}(t)\\ y(t) & = \mathit{Cx } (t) \end{array} \right \} }$$

(1)

where $E,A \in M = M_{n}(\mathbb{C})$, $B \in M_{n\times m}(\mathbb{C})$, $C \in M_{p\times n}(\mathbb{C})$, functional output-controllability character is considered. A simple test based in the computation of the rank of a certain constant matrix that can be associated to the system is presented.