@article{Aisagaliev_Ayazbayeva_2018, title={Investigation on absolute stability of multidimensional regulated systems. Aizerman problem}, volume={96}, url={https://bm.kaznu.kz/index.php/kaznu/article/view/563}, abstractNote={<p>with many nonlinearities is supposed. The motion equation of the regular system is reduced<br>to a special kind by nonsingular transformation which allows to present the nonlinearities as<br>functions of phase variables. Estimations of the phase variables and identities along solution of<br>the system are obtained for systems with limited resources. Estimations of the improper integrals<br>are found and conditions of the absolute stability in the space of constructive parameters of<br>the system are formulated. Possibility of the sector existence is considered, where Aizerman<br>problem has solution for regular systems with limited resources. It should be noted, that frequency<br>condition of the V.M.Popov absolute stability for systems with many nonlinearities has not any<br>geometrical interpretation, as in the one-dimensional case, and its verify is difficult problem.<br>Therefore development of the new method for investigation on absolute stability of regular systems<br>is topical. Distinctive feature of the supposed method of investigation on absolute stability from<br>known methods is that the conditions of the absolute stability are obtained without using Lyapunov<br>function and frequency theorem of V.A. Yakubovich.</p>}, number={4}, journal={Journal of Mathematics, Mechanics and Computer Science}, author={Aisagaliev S. А. and Ayazbayeva, A. M.}, year={2018}, month={Dec.}, pages={3–22} }