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Realization and Discretization of Asymptotically Stable Homogeneous Systems

Denis Efimov 1 Andrey Polyakov 1 Arie Levant 2 Wilfrid Perruquetti 3, 1
3 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : 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 non-zero 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.
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Denis Efimov, Andrey Polyakov, Arie Levant, Wilfrid Perruquetti. Realization and Discretization of Asymptotically Stable Homogeneous Systems. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2017, 62 (11), pp.5962 - 5969. ⟨10.1109/TAC.2017.2699284⟩. ⟨hal-01514350⟩

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