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                <term xml:lang="en">Averaged control</term>
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              <p>In this article we consider a linear finite dimensional system. Our aim is to design a control such that the output of the system reach a given target at a final time T &gt; 0. This notion is known as output controllability.We extend this notion to the one of long-time output controllability. More precisely, we consider the question: is it possible to steer the output of the system to some prescribed value in time T &gt; 0 and then keep the output of the system at this prescribed value for all times t &gt; T ? We provide a necessary and sufficient condition for this property to hold. Once the condition is satisfied, one can apply a feedback control that keeps the average fixed during a given time period. We also address the L2 -norm optimality of such controls.We apply our results to (long-time) averaged control problems.</p>
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