Zhumatov S. S.
Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1053-1063
We study the absolute stability of the program manifold of basic control systems with variable coefficients and stationary nonlinearities. The conditions of stability of basic systems are investigated in a neighborhood of a given program manifold. The nonlinearities satisfy the conditions of local quadratic relationship. Sufficient conditions for the absolute stability of the program manifold with respect to a given vector function are established by constructing the Lyapunov function. A method used to select the Lyapunov matrix is specified.
Ukr. Mat. Zh. - 2014. - 66, № 4. - pp. 558–565
Sufficient conditions for the asymptotic and uniform asymptotic stability of implicit differential systems in a neighborhood of the program manifold are established. Sufficient conditions of stability are also obtained for the known first integrals. A class of implicit systems for which it is possible to find the derivative of the Lyapunov function is selected.
Ukr. Mat. Zh. - 2010. - 62, № 6. - pp. 784–790
We establish sufficient conditions for the exponential stability of a program manifold of indirect control systems and conditions for the fast operation of a regulator, overcontrol, and monotone damping of a transient process in the neighborhood of the program manifold.
Ukr. Mat. Zh. - 2009. - 61, № 3. - pp. 418-424
We establish sufficient conditions for the absolute stability of a program manifold of control systems. In the case where the Jacobi matrix is degenerate, sufficient conditions for the absolute stability of a program manifold is obtained by reduction to the central canonical form.