ABSOLUTE STABILITY OF NON-LINEAR MANAGEMENT SYSTEMS

The problem of the absolute stability of systems, having a non-linear stationary part and non-linear elements in feed-back has been considered. We know about non-linear elements only that they belong to a some class. Cases of stationary and non-stationary non-linear elements have been considered separately. The standing problem about necessary and sufficient conditions of the existence of functions of Lyapunov from the class of Lurie - Postnikov has been solved for the case of stationary non-linear elements. Only sufficient conditions have been known earlier. New conditions of signdeterminacy of quadratic forms in a cone have been obtained for the solution of this problem. Applications of this problems to the stability of mechanical systems with one-sided connections have been considered. Necessary and sufficient conditions of the asymptotical stability of selector-linear differential inclusions have been obtained. The problem about the absolute stability of non-stationary management systems has been reduced to this problem. Two-dimensional, three-dimensional and general cases have been considered separately. Constructive necessary and sufficient conditions of the absolute stability have been obtained in all casesAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio