Reachability Analysis for Linear Hybrid Set-Dynamics Driven by Random Convex Compact Sets

This paper studies linear set-dynamics driven by random convex compact sets (RCCSs), where the parameter matrix evolves according to an underlying Markovian random process taking values in a finite set. We derive dynamics of the expectations of the associated reach sets. We establish that such expectations evolve according to coupled deterministic set–dynamics. We provide sufficient conditions for the convergence of the reach sets expectations. We also give conditions under which the reach sets remain asymptotically bounded with probability one. As an illustrative example, we apply our results to evaluate the expectations of the reach sets associated to the position of a quadrotor