Investigation on absolute stability of multidimensional regulated systems. Aizerman problem (Journal of Mathematics Mechanics and Computer Science, 2018)
with many nonlinearities is supposed. The motion equation of the regular system is reducedto a special kind by nonsingular transformation which allows to present the nonlinearities asfunctions of phase variables. Estimations of the phase variables and identities along solution ofthe system are obtained for systems with limited resources. Estimations of the improper integralsare found and conditions of the absolute stability in the space of constructive parameters ofthe system are formulated. Possibility of the sector existence is considered, where Aizermanproblem has solution for regular systems with limited resources. It should be noted, that frequencycondition of the V.M.Popov absolute stability for systems with many nonlinearities has not anygeometrical 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 systemsis topical. Distinctive feature of the supposed method of investigation on absolute stability fromknown methods is that the conditions of the absolute stability are obtained without using Lyapunovfunction and frequency theorem of V.A. Yakubovich.
Keywords: Absolute stability; nonsingular transformation; properties of the solutions; improper integrals; Aizerman problem; absolute stability sectors