Dynamics analysis of the set of trajectories on a product of convex compacts

Authors

  • A. A. Martynyuk S. P. Timoshenko Institute of Mechanics NAS of Ukraine, Kiev
  • L. M. Chernetskaya S. P. Timoshenko Institute of Mechanics NAS of Ukraine, Kiev
  • Yu. A. Martynyuk-Chernienko S. P. Timoshenko Institute of Mechanics NAS of Ukraine, Kiev

DOI:

https://doi.org/10.15407/dopovidi2016.09.044

Keywords:

comparison principle, equations with Hukuhara derivative, stability of the set of trajectories

Abstract

For a set of differential equations with Hukuhara derivative defined on a product of nonempty convex and compact spaces, the comparison principle and sufficient conditions of stability of a stationary motion are established. We use the vector Lyapunov-like function of a special structure.

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References

Aubin J.-P., Frankowska H. Set Valued Analysis, Basel: Birkhäser, 1990.

Matrosov V.M., Anapol'skii L.Yu., Vasil'yev S.N. Comparison method in mathematical theory of systems, Novosibirsk: Nauka, 1980.

Lakshmikantham V., Bhaskar T. G., Devi J. V. Theory of Set Differential Equations in a Metric Space, Melbourne: Florida Institute of Technology, 2005.

Martynyuk A. A. Stability of Motion. The Role of Multicomponent Liapunov's Functions, Cambridge: Cambridge Scientific Publishers, 2007.

Lakshmikantham V., Leela S., Martynyuk A. A. Stability Analysis of Nonlinear Systems, New York: Marcel Dekker, 1989.

Martynyuk A. A., Martynyuk-Chernienko Yu. A. Uncertain Dynamical Systems: Stability and Motion Control, Boca Raton: CRC Press, 2012.

Published

19.11.2024

How to Cite

Martynyuk, A. A., Chernetskaya, L. M., & Martynyuk-Chernienko, Y. A. (2024). Dynamics analysis of the set of trajectories on a product of convex compacts . Reports of the National Academy of Sciences of Ukraine, (9), 44–50. https://doi.org/10.15407/dopovidi2016.09.044