USING THE LYAPUNOV`S METHOD FOR EVALUATION  OF NANOSYSTEM STABILITY

P. Deeva; V. Deeva; V. Teterin; S. Slobodyan

doi:10.12737/20003

USING THE LYAPUNOV`S METHOD FOR EVALUATION OF NANOSYSTEM STABILITY

Published in Alternative energy sources in the transport-technological complex: problems and prospects of rational use of · Volume 3, Issue 2 · Pages 26–30 · Rubric: Primenenie nanotehnologiy v transportno-tehnologicheskom komplekse

DOI: https://doi.org/10.12737/20003

Received: 08.06.2016 Accepted: 08.06.2016 Published: 08.06.2016 Language of publication: RUS

Authors

P. Deeva

V. Deeva

V. Teterin

S. Slobodyan

P. Deeva

V. Deeva

V. Teterin

S. Slobodyan

ABSTRACT

When the nanoparticles move in pipe flow, there is a strong trend for particle coarsening. The prediction of cluster aggregation as well as the application of devices, which prevents coagulation and aggregation of the viscous nanoparticles in complex pipe systems, is of major importance in many processes. The article outlines the basic concepts of Lyapunov’s method for stability of dynamical nanosystem. In conclusion we summary the main empirical findings and provide method for performing a stability analysis.

KEYWORDS

evaluation, dynamics, stability, impact, Lyapunov’s method

1. Teterin V.S., Deeva V.S., Slobodyan S.M., Shcherban´ K.V. Optimal´nyy shar razdelitelya vyazkogo potoka [Tekst]. Al´ternativnye istochniki energii v transportno-tekhnologicheskom komplekse: problemy i perspektivy ratsional´nogo ispol´zovaniya. - 2016.- T. 3. № 1. - S. 138-141. - DOI:https://doi.org/10.12737/18577.

2. Deeva, V.S. Optimization of the parameters for disperser for separating particles of oil [Tekst] / V.S. Deeva, S.M. Slobodyan, V.S. Teterin. The 2nd International Conference on Industrial Engineering, 2016 (ICIE 2016), May 19-20, 2016; 2016. pp. 1-4.

3. Deeva, B.S. Entropiynyy podkhod k otsenke zhivuchesti sredstv kontrolya [Tekst] / B.S. Deeva, S.M. Slobodyan. Vestnik Altayskogo gosudarstvennogo agrarnogo universiteta. - 2015. - № 4 (126). - S. 121-128.

4. Deeva, B.S. Ustoychivost´ entropiynoy otsenki zhivuchesti sistem [Tekst]/ V.S. Deeva, S.A. Romanishina, S.M. Clobodyan. Izvestiya Tomskogo politekhnicheskogo universiteta. - 2013. - T. 322. № 2. - S. 67-72.

5. Slobodyan, S.M. Optimization of a bimorph drive in optical measuring systems with feedback [Tekst]/S.M. Slobodyan. Measurement Techniques. - 2003. -V. 46. No. 1. - P. 28-34.

6. Deeva, B.S. Zhivuchest´ kontakta preryvaemogo skol´zheniya [Tekst] / B.S. Deeva, M.S. Clobodyan, S.M. Slobodyan. Kontrol´. Diagnostika. - 2013. - № 6. - S. 59-65.

7. Nikitin, N.N. Kurs teoreticheskoy mekhaniki [Tekst] / N.N. Nikitin. - M.: Vysshaya shkola, 1990. - 607 s.

8. Butenin, N.V. Teoriya kolebaniy [Tekst] / N.V. Butenin. - M.: Vysshaya shkola, 1963.- 188 s.

9. Shaikhet, L. Lyapunov Functionals and Stability of Stochastic Difference Equations [Tekst] / L. Shaikhet. - Springer-Verlag: London Limited, 2011. - 384 p.

10. Prasad, B. Stability and Lyapunov exponents of a q-deformed map / B. Prasad, K. Katiyar. International Journal of Pure and Applied Mathematics. - 2015. - V.104, No. 4. - R. 509-516.

11. McCartney, M. Lyapunov exponent for multi-parameter tent and logistic maps / M. McCartney. Chaos. - 2011. - V. 21, No. 4. - R. 1-7.

12. Anbu, S. Design of adaptive controller based on Lyapunov stability for a CSTR / S. Anbu, N. Jaya. International Scholarly and Scientific Research and Innovation. - 2014. - V. 8, No. 1. - R. 176-179.

13. Astron, K.J. Adaptive Control / K.J. Astron, B. Wittenmark. 2nd edn. - New Delhi: Pearson Education, 2006. - 588 p.

14. Dorf, R.C. Modern Control Systems / R.C. Dorf, R.H. Bishop. 8th edn. - Singapore-New Delhi: Pearson Education Private Limited, Indian branch, 1999. - 420 r.

15. Pai, M.A. Energy function analysis for power system stability [Tekst] / M.A. Pai. - Norwel, MA: Kluwer, 1989. - 326 p.

16. Fouad, A.A. Power system transient stability analysis using the transient energy function method [Tekst] / A.A. Fouad, V. Vittal. - Englewood Cliffs: Prentice Hall, 1991. - 284 p.

17. Athay, T. A practical method for the direct analysis of transient stability [Tekst] / T. Athay, R. Podmore, S. Virmani. IEEE Trans. Power Appar. and Syst. - 1979. - V. 98, No. 2. - P. 573-584.

18. Chiang, H.D. A BCU method for direct analysis of power systems transient stability [Tekst] / H.D. Chiang, F.F. Wu, P.P. Varaiya. IEEE Trans. Power Syst. - 1994. - V. 9, No. 6. - P. 1194-1208.

19. Chiang, H.D. Foundations of PEBS method for power systems transient stability analysis [Tekst] / H.D. Chiang, F.F. Wu, P.P. Varaiya. IEEE Trans. Circuits and Systems. - 1988. - V. 35, No. 6. - P. 675-682.

20. Maria, G. Hibrid stability analysis [Tekst] / G. Maria, C. Tang, J. Kim. IEEE Trans. Power Systems. - 1990. - V. 5, No. 2. - R. 384-391.

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Editor-in-Chief, editorial board chair

GOST

Deeva P., Deeva V., Teterin V., Slobodyan S. USING THE LYAPUNOV`S METHOD FOR EVALUATION OF NANOSYSTEM STABILITY // Alternative energy sources in the transport-technological complex: problems and prospects of rational use of. 2016. no. 2. pp. 26-30. DOI: https://doi.org/10.12737/20003. (Date of access 14.10.2026).

MLA

P. Deeva, Deeva V., Teterin V., Slobodyan S.. "USING THE LYAPUNOV`S METHOD FOR EVALUATION OF NANOSYSTEM STABILITY." Alternative energy sources in the transport-technological complex: problems and prospects of rational use of 3.2 (2016): 26-30. DOI: https://doi.org/10.12737/20003.

APA

Deeva P., Deeva V., Teterin V., Slobodyan S. (2016). USING THE LYAPUNOV`S METHOD FOR EVALUATION OF NANOSYSTEM STABILITY. Alternative energy sources in the transport-technological complex: problems and prospects of rational use of, 3(2), 26-30. https://doi.org/10.12737/20003

Chicago

P. Deeva, Deeva V., Teterin V., Slobodyan S.. "USING THE LYAPUNOV`S METHOD FOR EVALUATION OF NANOSYSTEM STABILITY." Alternative energy sources in the transport-technological complex: problems and prospects of rational use of 3, no. 2 (2016): 26-30. https://doi.org/10.12737/20003.

WIKI

{{cite journal | author = Deeva P., Deeva V., Teterin V., Slobodyan S. | title = USING THE LYAPUNOV`S METHOD FOR EVALUATION OF NANOSYSTEM STABILITY | journal = Alternative energy sources in the transport-technological complex: problems and prospects of rational use of | year = 2016 | volume = 3 | issue = 2 | pages = 26-30 | doi = 10.12737/20003 }}

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