LIMIT SHAPES OF REACHABLE SETS OF SINGULARLY PERTURBED LINEAR CONTROL SYSTEMS
We study shapes of reachable sets of singularly perturbed linear control systems. The fast component of a phase vector is assumed to be governed by a hyperbolic linear system. We show that the shapes of reachable sets have a limit as the parameter of singular perturbation tends to zero. We also find a sharp estimate for the rate of convergence. A precise asymptotics for the support function of the normalized reachable sets is presented.