2019
Том 71
№ 10

All Issues

Zhumatov S. S.

Articles: 4
Article (Russian)

On the stability of a program manifold of control systems with variable coefficients

Zhumatov S. S.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1053-1063

UDC 517.956
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.

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.