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Dynamical Systems pp 57–69Cite as

The Ljapunov Vector Function Method in the Analysis of Stability and other Dynamic Properties of Nonlinear Systems

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 287))

Abstract

A method of analysis of some dynamic properties of nonlinear systems of various types developed at the Irkutsk Computer Center is given. Applications of this method showed that it has high efficiency, considerable advantages over other known methods of stability analysis of nonlinear systems, and a need to be expanded into a more general form. It has been possible to extend this method to abstract concepts of dynamics and control theory. The problem of deriving theorems from the vector of the Ljapunov function method for the dynamic properties of various types is discussed. Methods and algorithms for the construction and application of the Ljapunov vector function (LVF) are described.

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References

  • Matrosov, V.M. (1962), On the theory of stability, Appl. Math. Mech., 6.

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  • Matrosov, V.M. (1971), Ljapunov functions in the analysis of nonlinear interconnected systems, Simp. Math. V., 6, pp. 202–242 (Academic Press, New York, London).

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  • Matrosov, V.M. (1973), Comparison method in systems dynamics, Proceedings “Equa Diff-73”, Paris.

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  • Matrosov, V. M., Vassiliev, S.N., et al. (1981), The Algorithms of Theorem Derivations by the Ljapunov Vector Functions Method (Nauka, Novosibirsk). (In Russian).

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  • Matrosov, V.M. et al. (1984), The Ljapunov Functions Method and Its Applications (Nauka, Novosibirsk). (In Russian).

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  • Vassiliev, S.N. (1979), The derivation of theorem on dynamic properties, Algorithm Problem. Algebr. Syst. and Computers, pp. 3–35 (Irkutsk University, Irkutsk). (In Russian).

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Authors and Affiliations

  1. Irkutsk Computer Center of the Siberian Division of the USSR Academy of Sciences, USSR

    V. M. Matrosov

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  1. V. M. Matrosov
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Editors and Affiliations

  1. International Institute for Applied Systems Analysis, Schlossplatz 1, A-2361, Laxenburg, Austria

    Alexander B. Kurzhanski  & Karl Sigmund  & 

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© 1987 Springer-Verlag Berlin Heidelberg

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Matrosov, V.M. (1987). The Ljapunov Vector Function Method in the Analysis of Stability and other Dynamic Properties of Nonlinear Systems. In: Kurzhanski, A.B., Sigmund, K. (eds) Dynamical Systems. Lecture Notes in Economics and Mathematical Systems, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-00748-8_6

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  • DOI: https://doi.org/10.1007/978-3-662-00748-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17698-5

  • Online ISBN: 978-3-662-00748-8

  • eBook Packages: Springer Book Archive

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