The global stability of two-dimensional systems for controlling angular orientation

A two-dimensional dynamical system with an angular coordinate, describing t he operation of a two-position automatic steering device, the plane rotatio ns of a spacecraft controlled by an angular orientation system, and a phase -lock control frequency system with a proportional-plus-integral filter is considered. An analogue of the Barbashin-Krasovskii theorem is obtained for differential inclusions with angular coordinates. This is used to prove th e global stability of two-dimensional systems of angular orientation when t here is no external force moment. It is shown that, when there is a constan t external force moment in phase space, a region of initial conditions exis ts that corresponds to circular motions of a spacecraft. (C) 2001 Elsevier Science Ltd. All rights reserved.