Robust Control of Uncertain Switched Linear Systems based on Stochastic Reachability

This paper proposes an approach to algor it hmically synthesize control strategies for set-to-set transitions of uncertain discrete-time switched linear systems based on a combination of tree search and reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant hybrid control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over sequences of the discrete states and LMI-constrained semi-definite programming (SDP) problems to compute stabilizing controllers, while polytopic input constraints are considered. An example for illustration is included.