Automation and Remote Control

, Volume 78, Issue 1, pp 1–15 | Cite as

Stabilization of one class of nonlinear systems

  • V. I. KorobovEmail author
  • M. O. Bebiya
Nonlinear Systems


Consideration was given to the problem of stabilization for one class of systems that are nonlinear and uncontrollable in the first approximation. The stabilization problem was solved by considering the nonlinear approximation. The stabilizing control was obtained by the method of Lyapunov function which was constructed as a quadratic form. To determine matrix of this quadratic form, a singular matrix Lyapunov equation was solved. For the system of nonlinear approximation, the stabilizing control was determined explicitly. It was proved that the resulting control solves the problem of stabilizing the original nonlinear system. An ellipsoidal estimate of the attraction domain of the zero stationary point was given.

Key words

stabilization with respect to nonlinear approximation Lyapunov function method singular Lyapunov matrix equation 


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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.V.N. Karazin National UniversityKharkovUkraine

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