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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.
MSC:
93D15Stabilization of systems by feedback
39A10Additive difference equations
93C65Discrete event systems
93D99Stability of control systems
References:
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[4]Xu Daoyi, Simple criteria of stability for interval matrix, Acta Mathematica Sinica, 1996, 29(3): 309–312.
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[7]Liao Xiaoxin, Theory and Application of Stability for Dynamical Systems, Beijing: National Defence Industrial Publisher of China, 2000.
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