On the stabilization of the motion of uncertain affine systems

Authors

  • A.A. Martynyuk S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
  • L.N. Chernetskaya S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
  • Yu.A. Martynyuk-Chernienko S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv

DOI:

https://doi.org/10.15407/dopovidi2019.09.003

Keywords:

affine system, Lyapunov function method, nonlinear stabilizability, stability

Abstract

The article discusses affine systems with uncertain parameter values, for the stabilization of which the linear control is applied. The study of the stability and boundedness of the motion is carried out by the direct Lyapunov method. The concept of a pair of nonlinearly stabilized systems is introduced, and the sufficient conditions for the stability and boundedness of the motion are established, including the case of stability over a finite time in terval.

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References

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Martynyuk, A. A. (2015). Novel bounds for solutions of nonlinear differential equations. Appl. Math., No. 6, pp. 182-194. doi: https://doi.org/10.4236/am.2015.61018

Rao, M. R. M. (1963). Upper and lower bounds of the norm of solutions of nonlinear Volterra integral equations. Proc. Not. Acad. Sci. (India), No. 33, pp. 263-266.

Tsokos, C. P. &Rao, M. R. M. (1969). Finite time stability of control systems and integral inequalities. Bul. Inst. Politech. Lasi., 15(19). No. 1-2, pp. 105-112.

Corless, U. & Leitmann, G. (1989). Deterministic Control of Uncertain Systems via a Constructive Use of Lyapunov Stability Theory. Berlin: Springer.

Martynyuk, A. A. & Martynyuk-Chernienko, Yu. A. (2012). Uncertain Dynamical Systems: Stability and Motion Control. Boca Raton: CRC Press. doi: https://doi.org/10.1201/b11314

Blancin,i F. (2016). Lyapunov methods in robustness — an overview. Univ. di Udine, Italy (manuscript). 73 p.

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Published

24.04.2024

How to Cite

Martynyuk, A., Chernetskaya, L., & Martynyuk-Chernienko, Y. (2024). On the stabilization of the motion of uncertain affine systems . Reports of the National Academy of Sciences of Ukraine, (9), 3–11. https://doi.org/10.15407/dopovidi2019.09.003

Issue

No. 9 (2019): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

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