Abstract
The article considers the properties of a new type of solutions that arise in discontinuous dynamic systems. A specific feature of these solutions is the tangency of the phase velocity vectors to the manifold of the right-hand side discontinuities, instead of the transversal intersection of the manifold typically observed for ordinary sliding modes. The solutions identified in this case are high-order sliding modes, and the order of the mode is determined by the smoothness of tangency of the sliding manifold. Second-order sliding modes are considered in detail. Examples of systems with such modes are given; application of the theory to stabilization of uncertain dynamic systems is described. It is shown that the sensitivity of high-order sliding modes to small variations in the right-hand side of the discontinuous system is an order of magnitude higher than for ordinary sliding modes.
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Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie Sbornik Trudov, No. 2, pp. 39–70, 1993.
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Emel'yanov, S.V., Korovin, S.K. & Levant, A. High-order sliding modes in control systems. Comput Math Model 7, 294–318 (1996). https://doi.org/10.1007/BF01128162
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DOI: https://doi.org/10.1007/BF01128162