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Generalized quadratic lyapunov functions for nonlinear/uncertain systems analysis

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Perspectives in robust control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 268))

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Abstract

We consider the class of discrete-time nonlinear/uncertain systems described by the feedback connection of a linear time-invariant system and a “troublesome component,” i.e. either a static nonlinearity or a time-varying parametric uncertainty. We propose a generalized quadratic Lyapunov function for stability analysis of such systems. In particular, the Lyapunov function is given by a quadratic form of a vector that depends on the state in a specific nonlinear manner. Introducing a quadratic-form model of the troublesome component in the spirit of integral quadratic constraints, we obtain sufficient conditions for the existence of such Lyapunov functions that proves global/regional stability. The conditions are given in terms of linear matrix inequalities that can be numerically verified in polynomial time.

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Authors and Affiliations

  1. University of Virginia, 22904, Charlottesville, VA, USA

    Tetsuya Iwasaki

Authors
  1. Tetsuya Iwasaki
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Editor information

S.O. Reza Moheimani BSc, MengSc, PhD

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© 2001 Springer-Verlag London Limited

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Iwasaki, T. (2001). Generalized quadratic lyapunov functions for nonlinear/uncertain systems analysis. In: Moheimani, S.R. (eds) Perspectives in robust control. Lecture Notes in Control and Information Sciences, vol 268. Springer, London. https://doi.org/10.1007/BFb0110619

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  • DOI: https://doi.org/10.1007/BFb0110619

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-452-9

  • Online ISBN: 978-1-84628-576-9

  • eBook Packages: Springer Book Archive

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