Consistent Discretization of Finite-time Stable Homogeneous Systems

An algorithm of implicit discretization for generalized homogeneous system having discontinuity only at the origin is developed. It is based on transformation of the original system to an equivalent standard homogeneous system which admits implicit discretization preserving finite-time convergence property. The scheme is demonstrated for a version of the so-called “quasi-continuous” high-order sliding mode algorithm.

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