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On the existence of a solution of riccati equation and the mismatch threshold in practical stabilization of uncertain dynamical systems

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Mechanics and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 151))

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Abstract

This paper presents a sufficient condition for the existence of a symmetric positive definite solution of a Riccati equation that appears in the design of a practically stabilizing controller for mismatched uncertain dynamical systems. It is used to compare two existing methods for stabilizing mismatched systems; one that involves measure of mismatch and the other that uses the Riccati equation. The result indicates that, if the measure of mismatch is within the threshold of mismatch (which is a sufficient condition for the first method to be applicable), then a symmetric positive definite solution exists for the Riccati equation (which is a sufficient condition for the second method to be applicable). The type of Riccati equation under consideration also appears in Game Theory and H ∞ Optimal Control.

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Authors and Affiliations

  1. Department of Electrical Engineering, California State University, Long Beach, 1250 Bellflower Boulevard, 90840-8303, Long Beach, California

    F. Hamano

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  1. F. Hamano
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Editor information

J. M. Skowronski H. Flashner R. S. Guttalu

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© 1991 Springer-Verlag

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Hamano, F. (1991). On the existence of a solution of riccati equation and the mismatch threshold in practical stabilization of uncertain dynamical systems. In: Skowronski, J.M., Flashner, H., Guttalu, R.S. (eds) Mechanics and Control. Lecture Notes in Control and Information Sciences, vol 151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006724

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  • DOI: https://doi.org/10.1007/BFb0006724

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53517-1

  • Online ISBN: 978-3-540-46752-6

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