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Dynamics, Bifurcations, and Control pp 173–190Cite as

Feedback Stabilization and H ∞ Control of Nonlinear Systems Affected by Disturbances: the Differential Games Approach

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 273))

Abstract

In this paper we discuss the differential games approach to stability questions in control systems affected by disturbances. Our main focus will be on nonlinear H ∞ but we also mention other related problems. We review some existing results on necessary and sufficient conditions based on the existence of a suitably defined Lyapunov function for the system. Being our attention to nonlinear systems, we formulate our conditions allowing nonsmooth Lyapunov functions, using therefore the concept of viscosity solutions for nonlinear partial differential equations. We then present some new results based on an old natural idea recently brought to attention in stabilization of systems by [8], and show how, from semiconcave or just continuous Lyapunov functions one can construct a (discontinuous) feedback that solves the H ∞ problem in an appropriate sense.

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Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni, 7, 35131, Padova, Italy

    Pierpaolo Soravia

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  1. Pierpaolo Soravia
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Editors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Universitätsstraße, 86150, Augsburg, Germany

    Fritz Colonius

  2. Fachbereich Mathematik, J.W. Goethe-Universität, Postfach 11 19 32, 60054, Frankfurt am Main, Germany

    Lars Grüne

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© 2002 Springer-Verlag Berlin Heidelberg

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Soravia, P. (2002). Feedback Stabilization and H ∞ Control of Nonlinear Systems Affected by Disturbances: the Differential Games Approach. In: Colonius, F., Grüne, L. (eds) Dynamics, Bifurcations, and Control. Lecture Notes in Control and Information Sciences, vol 273. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45606-6_12

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  • DOI: https://doi.org/10.1007/3-540-45606-6_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42890-9

  • Online ISBN: 978-3-540-45606-3

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