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E. D. Sontag, “Comments on Integral Variants of Input-to-State Stability,” Systems and Control Letter, Vol. 34, No. 1, 1998, pp. 93-100. doi:10.1016/S0167-6911(98)00003-6

has been cited by the following article:

• TITLE: A New Uniformly Ultimate Boundedness Criterion for Discrete-Time Nonlinear Systems

  AUTHORS: Zhishuai Ding, Guifang Cheng

  KEYWORDS: Uniformly Ultimate Boundedness, Lyapunov Function, Discrete-Time Nonlinear Systems

  JOURNAL NAME: Applied Mathematics, Vol.2 No.11, November 30, 2011

  ABSTRACT: A new type criterion of globally uniformly ultimate boundedness for discrete-time nonlinear systems is introduced. In classical Lyapunov theory about globally uniformly ultimate boundedness, Lyapunov function is assumed to be positive definite and its difference at the every latter moment and the former moment is negative definite. In this paper the condition of difference of Lyapunov function is relaxed. Under the relaxed condition, the result of this paper can be considered as the extension of the classical Lyapunov theory about uniformly ultimate boundedness.