Realization and Discretization of Asymptotically Stable Homogeneous Systems

Denis Efimov, Andrey Polyakov, Arie Levant, Wilfrid Perruquetti

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Sufficient conditions for the existence and convergence to zero of numeric approximations to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that the explicit Euler method has certain drawbacks for the global approximation of homogeneous systems with nonzero degrees, whereas the implicit Euler scheme ensures convergence of the approximating solutions to zero. Properties of absolute and relative errors of the respective discretizations are investigated.

Original languageEnglish
Article number7914758
Pages (from-to)5962-5969
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number11
StatePublished - Nov 2017


  • Computer simulation
  • Lyapunov methods
  • System implementation

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