International Conference «Mathematical and Informational Technologies, MIT-2011»
(IX Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, August, 27–31, 2011

Budva, Montenegro, August, 31 – September, 5, 2011

Zhumatov S.S.  

Convergence property of control systems in the neighborhood of program manifold

The problem of construction of all the set of differential equations possessing by given integral manifold have been formulated and a method of solving this problem is given by Erugin N.P. Later on Erugin's method was developed for construction of stable system of differential equa-tions and nonlinear automatic control systems under given program manifold. It is known that realization of stability and other qualitative property of program manifold is required for construction program motion's systems. The problem of finding of convergence conditions of control systems in the neighborhood of program manifold is investigated with respect to the given vector-function in this paper. It is considered the material system subjected to external action, possessing by integral manifold, the motion of which described by control systems equations. Vector-function of control on deflection from given program satisfies local quadratic connection's conditions. Frequently and algebraically conditions of convergence conditions of control systems in the neighborhood of program manifold are established by the method of construction Lyapunov's function in the form of "quadratic form plus integral from of nonlinearity" and Popov's frequently criteria.


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