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On asympotic behavior of solutions to several classes of discrete dynamical systems

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Abstract

In this paper, a new complete and simplified proof for the Husainov-Nikiforova Theorem is given. Then this theorem is generalized to the case where the coefficients may have different signs as well as nonlinear systems. By these results, the robust stability and the bound for robustness for high-order interval discrete dynamical systems are studied, which can be applied to designing stable discrete control system as well as stabilizing a given unstable control system.

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References

  1. Husainov, D. J., Nikiforova, N. S., Stability for a difference equation with constant coefficients, Ukr. J. Mathematic (in Russian), 1999, 51(9): 1276–1280.

    Google Scholar 

  2. Khartionov, V. L., Asymptotic stability of an equilibrium position of a family of system of linear differential equation, Differential Equations, 1987, 14(11): 2086–2088.

    Google Scholar 

  3. Feng Chunbo, Calculation of eigenvalue and their distribution for linear systems, Science in China, Ser. E, 1999, 41(4): 443–448.

    Google Scholar 

  4. Xu Daoyi, Simple criteria of stability for interval matrix, Acta Mathematica Sinica, 1996, 29(3): 309–312.

    Google Scholar 

  5. Liao Xiaoxin, Li Lipeng, Algebraic criteria of stability for discrete dynamical systems, Acta Mathematica Scientia, 1986, 6(4): 375–383.

    Google Scholar 

  6. Liao Xiaoxin, Advance in robust stability for interval dynamical systems, Advances in Mathematics, 1992, 21(2): 168–184.

    MATH  MathSciNet  Google Scholar 

  7. Liao Xiaoxin, Theory and Application of Stability for Dynamical Systems, Beijing: National Defence Industrial Publisher of China, 2000.

    MATH  Google Scholar 

  8. Swaroop, D., Hedrick, J. K., String stability of interconnected systems, IEEE Trans. Automat. Cont., Vol. AC-AI, 1996, 349–357.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, 430074, Wuhan, China

    Xiaoxin Liao

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  1. Xiaoxin Liao
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Liao, X. On asympotic behavior of solutions to several classes of discrete dynamical systems. Sci. China Ser. A-Math. 45, 432–442 (2002). https://doi.org/10.1007/BF02872331

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  • DOI: https://doi.org/10.1007/BF02872331

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