On Stabilization of Switching Linear Systems

This paper addresses the problem of controlling a continuous-time linear system that may switch among different modes taken from a finite set. The current mode of the system is supposed to be unknown. Moreover, unknown but bounded disturbances are assumed to affect the dynamics as well as the measurements. The proposed methodology is based on a minimum-distance mode estimator which orchestrates controller switching according to a dwell-time switching logic. Provided that the controllers are designed so as to ensure a certain mode observability condition and that the plant switching signal is slow on the average, the resulting control system turns out to be exponentially input-to-state stable.