Investigation on absolute stability of multidimensional regulated systems. Aizerman problem

Abstract

with many nonlinearities is supposed. The motion equation of the regular system is reduced
to a special kind by nonsingular transformation which allows to present the nonlinearities as
functions of phase variables. Estimations of the phase variables and identities along solution of
the system are obtained for systems with limited resources. Estimations of the improper integrals
are found and conditions of the absolute stability in the space of constructive parameters of
the system are formulated. Possibility of the sector existence is considered, where Aizerman
problem has solution for regular systems with limited resources. It should be noted, that frequency
condition of the V.M.Popov absolute stability for systems with many nonlinearities has not any
geometrical interpretation, as in the one-dimensional case, and its verify is difficult problem.
Therefore development of the new method for investigation on absolute stability of regular systems
is topical. Distinctive feature of the supposed method of investigation on absolute stability from
known methods is that the conditions of the absolute stability are obtained without using Lyapunov
function and frequency theorem of V.A. Yakubovich.