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On State-dependent Discretization of Stable Homogeneous Systems


Conditions for the existence and convergence to zero of numeric approximations with state-depend step of discretization to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that for a sufficiently small discretization step the convergence of the approximating solutions to zero can be guaranteed globally in a finite or a fixed time, but in an infinite number of discretization iterations. It is proven that the absolute and relative errors of the respective discretizations are globally bounded functions. Efficiency of the proposed discretization algorithms is demonstrated by the simulation of the super-twisting system.


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hal-01888564 , version 1 (05-10-2018)



Denis Efimov, Andrey Polyakov, Alexander Yu Aleksandrov. On State-dependent Discretization of Stable Homogeneous Systems. CDC 2018 - 57th IEEE Conference on Decision and Control, Dec 2018, Miami Beach, FL, United States. ⟨10.1109/CDC.2018.8618657⟩. ⟨hal-01888564⟩
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