**AUTHORS:**Maria Isabel Garcia-Planas

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**ABSTRACT:**
Due to the significant role played by singular systems in the form Ex˙(t) = Ax(t), on mathematical
modeling of science and engineering problems; in the last years recent years its interest in the descriptive analysis
of its structural and dynamic properties. However, much less effort has been devoted to studying the exact controllability
by measuring the minimum set of controls needed to direct the entire system Ex˙(t) = Ax(t) to any
desired state. In this work, we focus the study on obtaining the set of all matrices B with a minimal number of
columns, by making the singular system Ex˙(t) = Ax(t) + Bu(t) controllable.

**KEYWORDS:**
Controllability, exact controllability, eigenvalues, eigenvectors, singular linear systems

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