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Piecewise-linear functions in robust control

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Robust Control via Variable Structure and Lyapunov Techniques

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 217))

Abstract

In this contribution we have described basic properties of piecewise-linear (polyhedral) Lyapunov functions in the control of systems with parametric uncertainties and unknown but bounded disturbances. We have shown some numerical procedures for their synthesis and we have presented some applications. It is important to remark that using this kind of functions may require a nontrivial computational effort due to the complexity of their representation. This problem is important, but it may be considered not very crucial if we take into account the modern computer technology.

There are still open problems that may be of interest for future research. For instance, so far the considered compensators are of the state feedback type, while in many applications only output feedback is available. Another important problem is to reduce the complexity of the compensators which can be associated to Lyapunov functions. A further important problem is to find numerical efficient algorithms for the generation of Lyapunov functions of the polyhedral type.

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Authors
  1. Franco Blanchini
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  2. Stefano Miani
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Editor information

Franco Garofalo Luigi Glielmo

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© 1996 Springer-Verlag London Limited

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Blanchini, F., Miani, S. (1996). Piecewise-linear functions in robust control. In: Garofalo, F., Glielmo, L. (eds) Robust Control via Variable Structure and Lyapunov Techniques. Lecture Notes in Control and Information Sciences, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027568

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  • DOI: https://doi.org/10.1007/BFb0027568

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76067-2

  • Online ISBN: 978-3-540-40946-5

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