eng Oriental Scientific Publishing Company Biosciences Biotechnology Research Asia 0973-1245 2015-04-28 12 1 779 788 6153 article Lidiya Alekseevna Bondarenko 1 Afanasy Vladimirovich Zubov 1 Alexandra Fedorovna Zubova 1 Sergey Vladimirovich Zubov 1 Vyacheslav Borisovich Orlov 1 Saint Petersburg State University, University pr. 35, St.Petersburg, 198504, Russia The work is devoted to development of mathematical apparatus which facilitates analysis of stability of control systems with aftereffect including analytical methods and numerical algorithms for solution of stability problems by the first non-linear approximation and problems of robust stability for these systems. The article discusses the issues of existence and stability of stationary modes in dynamic systems with aftereffect, as well as influence of external limited impacts on these modes. Criteria of stability have been obtained based on the first non-linear approximation of quasilinear systems with aftereffect and systems with aftereffect with the degree of non-linearity higher than the first degree. https://www.biotech-asia.org/vol12no1/stability-of-quasilinear-dynamic-systems-with-after-effect/ Functional; Constant; Condition; Inequality; System; solution; integral equation; structural minimization