Stabilization and tracking for switching linear systems under unknown switching sequences

This paper describes recent progress in the study of switching linear systems i.e. linear systems whose dynamics can switch among a family of possible configurations/modes. The attention is focused on those classes of switching systems governed by unknown switching sequences. For this case, we address the problem of devising suitable control actions able to stabilize the plant and regulate its output about a desired reference trajectory. The approach considered in this paper consists in designing a suitable family of feedback controllers and a mode-estimator that at any time determines which candidate controller has to be placed in the feedback loop on the grounds of a real-time estimate of the current plant mode. It is shown that, even if a correct reconstruction of the plant mode from the measured data is not always possible, under certain conditions, exponential stability of the closed-loop can be guaranteed for any slow-on-the-average plant switching sequence.