2019
Том 71
№ 1

All Issues

Zhumatov S. S.

Articles: 3
Brief Communications (Russian)

Asymptotic Stability of Implicit Differential Systems in the Vicinity of Program Manifold

Zhumatov S. S.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Exponential stability of a program manifold of indirect control systems

Zhumatov S. S.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Russian)

Stability of a program manifold of control systems with locally quadratic relations

Zhumatov S. S.

↓ Abstract   |   Full text (.pdf)

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.