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Regularization of Second Order Sliding Mode Control Systems

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Modern Sliding Mode Control Theory

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 375))

Abstract

The numerical representation of singular systems [1], with index greater than two and inconsistent initial conditions, presents common features with the implementation of higher order sliding motions, [2], [3]. Indeed higher order sliding modes can be viewed as a way to achieve constrained motions, often expressible as an output-zeroing problem after a transient of finite duration [4]. The choice of the sliding output is the first step of a sliding mode design process (e.g. invariance [5]). If the actual control affects the time derivative of the sliding output, starting from a certain order k ≥ 1 , the corresponding constrained motion, if attainable, is said to be a k-th order sliding motion [6], [7], [8], [9], [10]. The notion of sliding order is equivalent to the one of relative degree [4].

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Author information

Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, University of Cagliari, Piazza d’Armi, 09123, Cagliari, Italy

    Giorgio Bartolini

  2. Institute of Intelligent Systems for Automation, National Research Council of Italy (ISSIA-CNR), Via De Marini, 6, 16149, Genoa, Italy

    Elisabetta Punta

  3. Department of Mathematics, University of Genoa, Via Dodecaneso, 35, 16146, Genoa, Italy

    Tullio Zolezzi

Authors
  1. Giorgio Bartolini
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  2. Elisabetta Punta
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  3. Tullio Zolezzi
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Editor information

Giorgio Bartolini Leonid Fridman Alessandro Pisano Elio Usai

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Bartolini, G., Punta, E., Zolezzi, T. (2008). Regularization of Second Order Sliding Mode Control Systems. In: Bartolini, G., Fridman, L., Pisano, A., Usai, E. (eds) Modern Sliding Mode Control Theory. Lecture Notes in Control and Information Sciences, vol 375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79016-7_1

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  • DOI: https://doi.org/10.1007/978-3-540-79016-7_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79015-0

  • Online ISBN: 978-3-540-79016-7

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