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

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Abstract

We have seen in Chapter 5 that there are many linear systems that are not stable. In this chapter we study the problem of stabilizing an unstable system using an appropriate compensator. Not all systems are stabilizable. We characterize all stabilizable systems and give a parametrization of all compensators that stabilize such systems. An important role is played by identifying a linear system with its graph. As in Chapter 4, we assume that time is discrete.

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References

  1. Foias, C., Georgiou, T., Smith, M., Robust stability of feedback systems: A geometric approach using the gap metricSIAM J. Cont and Optim.31(b) (1993), 1518–1537.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  3. Dale, W., Smith, M., Stabilizability and existence of system representations for discrete-time time-varying systemsSIAM J. Cont and Optim.31(b) (1993), 1538–1557.

    Article  MathSciNet  MATH  Google Scholar 

  4. Smith, M.On stabilization and the existence of coprime factorizationsIEEE Trans. Aut. Cont.34 (1989), 1005–1007.

    Article  MATH  Google Scholar 

  5. Feintuch, A., Coprime factorization of discrete time-varying systemsSystem Control Lett.7 (1986), 49–50.

    Article  MathSciNet  MATH  Google Scholar 

  6. Arveson, W., Interpolation problems in nest algebrasJ. Funct. Anal.20 (1975), 208–233.

    Article  MathSciNet  MATH  Google Scholar 

  7. Feintuch, A., Saeks, R.System Theory: A Hilbert Space ApproachNew York, Academic Press, 1982.

    MATH  Google Scholar 

  8. Jones, P., Marshall, D., Wolff, T., Stable rank of the disc algebraProc. AMS96 (1986), 603–604.

    Article  MathSciNet  MATH  Google Scholar 

  9. Halanay, A., Ionescu, V.Time-varying Discrete Linear Systems, OT68, Basel, Birkhäuser-Verlag, 1994.

    Book  Google Scholar 

  10. Feintuch, A., Strong graph representations for linear time-varying systemsLinear Alg. and Applic.203–204 (1994), 385–399.

    Google Scholar 

  11. Treil, S., The stable rank of the algebraH ∞equals 1J. Funct. Anal., 109 (1992), 130–154.

    Article  MathSciNet  MATH  Google Scholar 

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© 1998 Springer Science+Business Media New York

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Feintuch, A. (1998). Stabilization. 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_6

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  • DOI: https://doi.org/10.1007/978-1-4612-0591-3_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6829-1

  • Online ISBN: 978-1-4612-0591-3

  • eBook Packages: Springer Book Archive

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