Open AccessABSOLUTE STABILITY OF A PROGRAM MANIFOLD OF NON-AUTONOMOUS BASIC CONTROL SYSTEMS
Author(s) -
S. S. Zhumatov
Publication year - 2018
Language(s) - English
DOI - 10.32014/2018.2518-1726.15
Subject(s) - manifold (fluid mechanics) , mathematics , lyapunov function , center manifold , nonlinear system , stability (learning theory) , invariant manifold , vector field , function (biology) , inverse , quadratic equation , mathematical analysis , computer science , geometry , physics , mechanical engineering , hopf bifurcation , quantum mechanics , machine learning , engineering , bifurcation , evolutionary biology , biology
In this paper the inverse dynamics problemisstudied: for a given manifold restore a force field, which lies in the tangent subspace to manifold. One of the general inverse problems of dynamics is solved: the corresponding system of differential equations is but as well as the stability is considered. This inverse problem is very important for a variety of mathematical models mechanics.Absolutestability of a program manifold of nonautonomous basic control systems with stationary nonlinearity is investigated.Theproblem of stability of the basic control systems is considered in the neighborhood of a program manifold. Nonlinearitysatisfies to conditions of localquadratic relations. The sufficient conditions of the absolute stability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function, in the form "quadratic form plus an integral from nonlinearity". The obtained results are used to solve the problem of the synthesis of high-speed regulators.