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On the quantitative characterization of approximate decentralized fixed modes using transmission zeros

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Abstract

The spectrum of a linear time-invariant multivariable system, using decentralized linear time-invariant controllers, can only be assigned to a symmetric set of complex numbers that include the decentralized fixed modes (DFM). Hence only systems with stable DFM can be stabilized. Although the concept of DFM characterizes when a decentralized controller can stabilize a system, it gives no indication of howhard it is to effect such a stabilization. A system is considered hard to stabilize if large controller gains are required. Modes that are hard to shift are termedapproximate decentralized fixed modes. In this paper two new assignability measures which quantify the difficulty of shifting a mode are derived. The first is coordinate invariant and is based on the distance between a mode and a set of transmission zeros. The second is coordinate dependent and is based on the minimum singular value of a set of transmission zero matrices.

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Author notes

  1. A. F. Vaz

    Present address: Bell-Northern Research Ltd, Station C, P.O. Box 3511, K1Y 4H7, Ottawa, Ontario, Canada

Authors and Affiliations

  1. Department of Electrical Engineering, University of Toronto, M5S 1A4, Toronto, Ontario, Canada

    A. F. Vaz & E. J. Davison

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  1. A. F. Vaz
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  2. E. J. Davison
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Additional information

This work has been supported by the Natural Sciences are Engineering Research Council of Canada under Grant No. A4396.

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Vaz, A.F., Davison, E.J. On the quantitative characterization of approximate decentralized fixed modes using transmission zeros. Math. Control Signal Systems 2, 287–302 (1989). https://doi.org/10.1007/BF02551388

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  • DOI: https://doi.org/10.1007/BF02551388

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