Probabilistic controllability analysis of sampled-data/discrete-time piecewise affine systems

This paper proposes a new approach to solve the controllability (reachability) problem of the sampled-data/discrete-time piecewise affine systems. First, an algebraic characterization for the system to be controllable/reachable is derived. Next, based on this characterization, an approach to determine if the system is controllable/reachable in a probabilistic sense is proposed based on a randomized algorithm. Finally, it is shown by numerical examples that the proposed approach is useful.