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On asymptotic behavior of solutions to several classes of discrete dynamical systems. (English) Zbl 1107.93029
Summary: 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.

93D15Stabilization of systems by feedback
39A10Additive difference equations
93C65Discrete event systems
93D99Stability of control systems
Full Text: DOI
[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. · Zbl 0979.39006 · doi:10.1007/BF02514459
[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.
[3] Feng Chunbo, Calculation of eigenvalue and their distribution for linear systems, Science in China, Ser. E, 1999, 41(4): 443--448. · Zbl 0912.93028 · doi:10.1007/BF02917017
[4] Xu Daoyi, Simple criteria of stability for interval matrix, Acta Mathematica Sinica, 1996, 29(3): 309--312. · Zbl 0604.34031
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[6] Liao Xiaoxin, Advance in robust stability for interval dynamical systems, Advances in Mathematics, 1992, 21(2): 168--184. · Zbl 0757.93066
[7] Liao Xiaoxin, Theory and Application of Stability for Dynamical Systems, Beijing: National Defence Industrial Publisher of China, 2000. · Zbl 0956.65067
[8] Swaroop, D., Hedrick, J. K., String stability of interconnected systems, IEEE Trans. Automat. Cont., Vol. AC-AI, 1996, 349--357. · Zbl 0848.93054 · doi:10.1109/9.486636