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Robustness of Time-Varying Systems

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Robust Control Theory in Hilbert Space

Part of the book series: Applied Mathematical Sciences ((AMS,volume 130))

Abstract

Consider the usual feedback system with plant L and controllerC, both in L. It is hypothesized thatLis not fixed but belongs to some setB. Therobust stability problem isto find, if one exists, a controller C that achieves internal stability for everyL∈B. In this generality the robust stability problem remains unsolved.

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References, Notes, and Remarks

  1. Georgiou, T., Smith, M., Optimal robustness in the gap metricIEEE Trans. Aut. Cont.35 (1990), 673–686.

    Article  MathSciNet  MATH  Google Scholar 

  2. Vidyasagar, M., Kimura, H., Robust controllers for uncertain linear multivariable systemsAutomatica22 (1986), 85–94.

    Article  MATH  Google Scholar 

  3. Vidyasagar, M. S.Control System Synthesis: A Factorization ApproachCambridge, Mass., MIT Press, 1985.

    MATH  Google Scholar 

  4. McFarlane, D. C., Glover, K., Robust Controller Design Using Normalized Coprime Factor Plant Descriptions, Springer-VerlagLecture Notes in Control and Information Sciences138, 1990.

    Book  Google Scholar 

  5. Feintuch, A., Robustness for time-varying systemsMCSS6 (1993), 247–263.

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  6. Shamma, J., The necessity of the small-gain theorem for time-varying and non-linear systemsIEEE Trans. Aut. Cont.36, 10 (1991), 1138–1147.

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  7. Shamma, J., Robust stability with time-varying structured uncertaintyIEEE Trans. Aut. Cont.39, 4 (1994), 714–724..

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  8. Feintuch,A. Markus,A., The structured norm of a Hilbert space operator with respect to a given algebra of operators,preprint.

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© 1998 Springer Science+Business Media New York

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Feintuch, A. (1998). Robustness of Time-Varying Systems. In: Robust Control Theory in Hilbert Space. Applied Mathematical Sciences, vol 130. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0591-3_8

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  • DOI: https://doi.org/10.1007/978-1-4612-0591-3_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6829-1

  • Online ISBN: 978-1-4612-0591-3

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