Discretization of Asymptotically Stable Homogeneous Systems by Explicit and Implicit Euler Methods

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.
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Denis Efimov, Andrey Polyakov, Arie Levant, Wilfrid Perruquetti. Discretization of Asymptotically Stable Homogeneous Systems by Explicit and Implicit Euler Methods. Proc. 55th IEEE Conference on Decision and Control (CDC), Dec 2016, Las Vegas, United States. ⟨hal-01371275⟩

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