Nonsmooth mapping of linear control systems

This paper deals with linear control systems of a special form. The main go al of the paper is to find the exact analytic solution of the time-optimal control problem for an arbitrary linear control system with constant coeffi cients using the analytic solution of this problem for the canonical system . For this aim, we construct a certain nonsmooth mapping between the 0-cont rollability sets of the given systems. In other words, by means of this map ping, we investigate the equivalence of the systems with the same qualitati ve behavior in a neighborhood of the stationary point.