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Stabilization and Optimal Control of Nonlinear Systems Homogeneous-in-the-Input

  • D. H. Jacobson

Abstract

Stabilizing and control strategies are presented for nonlinear and bilinear systems -which are homogeneous-In-the-input. For this class of systems It Is demonstrated that nonlinear controllers can be synthesized, which optimize a wide variety of performance criteria. These controllers produce asymptotic stability also in the interesting cases in which constant controllers fail to stabilize the systems. Extensions to non-homogeneous systems are given.

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References

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    Bruni, C., Di Pillo, G. & Koch, G. Bilinear systems: an appealing class of “nearly linear” systems in theory and applications. IEEE Trans. Automatic Control, AC-19, No. 4 1974, pp. 334–348.CrossRefGoogle Scholar
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    Kalman, R.E. Contributions to the theory of optimal control. Bol. Soc. Mat. Mexicana, 5, 1960, pp. 102–119.Google Scholar
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    Ionescu, T. & Monopoli, R.V. On the stabilization of bilinear systems via hyperstability. IEEE Trans. Automatic Control, AC-20, 1975, pp. 280–284.CrossRefGoogle Scholar
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    Hahn, W. Stability of motion. Springer Verlag, Berlin, Heidelberg, New York, 1967.Google Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • D. H. Jacobson
    • 1
  1. 1.National Research Institute for Mathematical SciencesPretoriaSouth Africa

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