**AUTHORS :**M. Isabel Garcia-Planas

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**ABSTRACT :**
In recent years there has been growing interest in the descriptive analysis of ℓ-order time invariant linear dynamical system xℓ = Aℓ-1xℓ-1 + ... + A0x0 where Ai are square complex matrices and xi denotes the i-th derivative of x. We are interested to mesure the minimum number of controls B that are needed in order to make the system xℓ = Aℓ-1xℓ-1 + ... + A0x0 + Bu controllable.

**KEYWORDS :**
ℓ-order time invariant linear dynamical system, Controllability, Exact controllability

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