On the construction of a family of Lyapunov functions for generalized systems

Summary (translated from the Russian): "We construct a family of Lyapunov functions for a very wide class of material systems, including mechanical and nonmechanical systems. We consider some applications of these functions. par "Earlier [Vestn. Ross. Univ. Druzhby Narod. Ser. Prikl. Mat. Inform. {bf 1995}, no. 1, 9--12; per bibl.] we constructed a family of Lyapunov functions to study the local stability of the unperturbed motion of mechanical systems. In another paper [Vestn. Ross. Univ. Druzhby Narod. Ser. Prikl. Mat. Inform. {bf 1998}, no. 1, 16--21; per bibl.] we used that approach to construct mechanical systems with programmed motion that is globally asymptotically stable. In the present paper we extend those results to a wider class of material systems, including both mechanical and nonmechanical systems. In addition, the family of Lyapunov functions constructed can be used to improve the quality of the transient process by means of optimal control, in particular, the stabilization of the programmed motion of a rigid body with a fixed point."