2019
Том 71
№ 6

All Issues

Dudzyanyi S. I.

Articles: 2
Article (Ukrainian)

On the stability of a trivial invariant torus of one class of impulsive systems

Dudzyanyi S. I., Perestyuk N. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 3. - pp. 338–349

We consider the problem of asymptotic stability of the trivial invariant torus of one class of impulsive systems. Sufficient criteria of asymptotic stability are obtained by the method of freezing in one case, and by the direct Lyapunov method for the investigation of stability of solutions of impulsive systems in another case.

Article (Ukrainian)

On the stability of an invariant torus

Dudzyanyi S. I., Perestyuk N. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1212-1222

We consider the problem of the asymptotic stability for trivial invariant torus of a linear extension of dynamical system on a torus. We formulate and prove sufficient criteria of asymptotic stability and study conditions for the existence and uniqueness of the Lyapunov functions of fixed sign.