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
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.
Vidyasagar, M.Control System Synthesis: A Factorization ApproachCambridge, Mass., MIT Press, 1985.
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.
Smith, M.On stabilization and the existence of coprime factorizationsIEEE Trans. Aut. Cont.34 (1989), 1005–1007.
Feintuch, A., Coprime factorization of discrete time-varying systemsSystem Control Lett.7 (1986), 49–50.
Arveson, W., Interpolation problems in nest algebrasJ. Funct. Anal.20 (1975), 208–233.
Feintuch, A., Saeks, R.System Theory: A Hilbert Space ApproachNew York, Academic Press, 1982.
Jones, P., Marshall, D., Wolff, T., Stable rank of the disc algebraProc. AMS96 (1986), 603–604.
Halanay, A., Ionescu, V.Time-varying Discrete Linear Systems, OT68, Basel, Birkhäuser-Verlag, 1994.
Feintuch, A., Strong graph representations for linear time-varying systemsLinear Alg. and Applic.203–204 (1994), 385–399.
Treil, S., The stable rank of the algebraH ∞equals 1J. Funct. Anal., 109 (1992), 130–154.
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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
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