We study, in the spirit of [1], reachable sets for singularly perturbed linear control systems. The fast component of the phase vector is assumed to be governed by a strictly stable linear system. It… (More)

We study the limit behavior of reachable sets for time-invariant linear control systems under two types of the control bounds: the geometric bounds, and the bound for the total impulse. Our main… (More)

The problem of minimum-time damping of a pendulum is a classical problem of control theory. In the linear case, described by the equation ẍ+ x = u, |u| ≤ 1, its solution is stated in [1]. The optimal… (More)

The paper is concernedwith small-time reachable sets of a linear dynamical system under integral constraints on control. The main result is the existence of a limit shape of the reachable sets as… (More)

We present explicit formulas for ellipsoids bounding reachable sets for linear control dynamic systems with geometric bounds on control. We study both locally and globally optimal ellipsoidal… (More)

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… (More)