Switching Control of Stochastic Linear Systems: Stability and Performance Results∗

In presence of large uncertainty, traditional methodologies based on a single controller do not provide, in general, satisfactory performance when applied to any system in the uncertainty set, and may not even guarantee stability. A way to address this problem is to consider a set of candidate controllers and design a supervisor that appropriately orchestrates the switching among them, based on the data collected from the controlled system. The analysis of the resulting hybrid switched control system requires specialized tools. In this paper, we consider the switching control of a class of stochastic linear system affected by a possibly unbounded noise. We study and compare two supervisory control schemes adopting respectively the dwell time and the hysteresis-based switching logic. We prove that they both stabilize the switched control system. We also show that self-optimality can be achieved in the dwell time switching scheme by adding an asymptotically vanishing dither noise to the control input.