Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 57, Issue 1, Pages 78-103Publisher
SIAM PUBLICATIONS
DOI: 10.1137/18M1197345
Keywords
differential inclusions; finite-time control; discrete-time systems; Lyapunov stability; homogeneous systems
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Funding
- French National Research Agency (ANR) [ANR-18-CE40-0008 DIGITSLID]
- Government of Russian Federation [08-08]
- Ministry of Education and Science of Russian Federation [14.Z50.31.0031]
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Algorithms of implicit discretization for generalized homogeneous systems having a possible discontinuity only at the origin are developed. They are based on the transformation of the original system to an equivalent one which admits an implicit or a semi-implicit discretization scheme preserving the stability properties of the continuous-time system. Namely, the discretized model remains finite-time stable (in the case of negative homogeneity degree) and practically fixed-time stable (in the case of positive homogeneity degree). The theoretical results are supported with numerical examples.
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