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Stability of Hybrid Systems Using LMIs — A Gear-Box Application

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Book cover Hybrid Systems: Computation and Control (HSCC 2000)

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Abstract

This paper includes an application consisting of an automatic gear-box and cruise controller which naturally is modelled as a hybrid system including state jumps in the continuous state of the controller. Motivated by this application, we extend existing stability results to include state jumps as well. The proposed stability results are based on Lyapunov techniques. The search for the (piecewise quadratic) Lyapunov functions is formulated as a linear matrix inequality (LMI) problem. It is shown how the proposed stability analysis is applied to the automatic gear-box and cruise controller.

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Author information

Authors and Affiliations

  1. Control Engineering Lab, Chalmers University of Technology, S-412 96, Gothenburg, Sweden

    Stefan Pettersson & Bengt Lennartson

Authors
  1. Stefan Pettersson
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  2. Bengt Lennartson
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Editor information

Editors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Nancy Lynch

  2. Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15235, USA

    Bruce H. Krogh

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© 2000 Springer-Verlag Berlin Heidelberg

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Pettersson, S., Lennartson, B. (2000). Stability of Hybrid Systems Using LMIs — A Gear-Box Application. In: Lynch, N., Krogh, B.H. (eds) Hybrid Systems: Computation and Control. HSCC 2000. Lecture Notes in Computer Science, vol 1790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46430-1_32

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  • DOI: https://doi.org/10.1007/3-540-46430-1_32

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67259-3

  • Online ISBN: 978-3-540-46430-3

  • eBook Packages: Springer Book Archive

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