Applications of a family of Lyapunov functions

A procedure for constructing a family of Lyapunov functions, which enable o ne to obtain criteria for asymptotic stability in the first approximation, is proposed for the systems of differential equations for the motion of a m aterial system of very general form. The problem of constructing control sy stems which ensure asymptotic stability "in the large" and the problem of i mproving the quality of the transient are considered. Examples are given of the use of the proposed procedure in the problem of stabilizing the planar motions of a satellite in an elliptic orbit and in the problem of stabiliz ing the programmed motion of a mathematical pendulum with a moving suspensi on point and of a gyropendulum on a moving base. (C) 2001 Elsevier Science Ltd.;Ali rights reserved.