Martin Lazar, Jerôme Lohéac. Output controllability in a long-time horizon. Automatica, Vol. 113 (2020). DOI: 10.1016/j.automatica.2019.108762
Abstract. 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. 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 and then keep the output of the system at this prescribed value for all times ? 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-norm optimality of such controls. We apply our results to (long-time) averaged control problems.