Applied Physics and Mathematics Annotation << Back THE ESTIMATION OF STABILITY OF NONLINEAR POLYNOMIAL CONTROL SYSTEMS BASED ON THE METHOD OF GROBNER BASES S.N. CHUKANOV, I.S. CHUKANOV The paper discusses methods for estimating stability with Lyapunov functions, used for nonlinear polynomial control systems, based on the method of Grobner bases. Buchberger’s algorithm is used to determine the Gröbner basis, which is implemented in symbolic computation programs for solving systems of nonlinear polynomial equations. The use of the Grobner basis for finding solutions of a nonlinear system of polynomial equations is considered, similar to the application of the Gauss method for solving a system of linear equations. The equilibrium states of a nonlinear polynomial system are determined as solutions of a nonlinear system of polynomial equations. The application of the Gröbner basis method for estimating the attraction domain of a nonlinear dynamic system with respect to the equilibrium point is considered. The use of Grobner bases in the gradient method for finding the Lyapunov function of a nonlinear dynamical system is considered. The coordination of input-output signals of the system based on the construction of Gröbner bases is considered. Keywords: nonlinear systems, polynomial systems, Lyapunov functions, Gröbner bases. DOI: 10.25791/pfim.04.2021.1202 Pp. 03-09.