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Root locations of an entire polytope of polynomials: It suffices to check the edges

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Abstract

The presence of uncertain parameters in a state space or frequency domain description of a linear, time-invariant system manifests itself as variability in the coefficients of the characteristic polynomial. If the family of all such polynomials is polytopic in coefficient space, we show that the root locations of the entire family can be completely determined by examining only the roots of the polynomials contained in the exposed edges of the polytope. These procedures are computationally tractable, and this criterion improves upon the presently available stability tests for uncertain systems, being less conservative and explicitly determining all root locations. Equally important is the fact that the results are also applicable to discrete-time systems.

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Author notes

  1. Huang Lin (Visiting Scholar)

    Present address: Department of Methemmtics and Statistics, University of Massachusetts, 01003, Amherst, Massachusetts, U.S.A.

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Massachusetts, 01003, Amherst, Massachusetts, U.S.A.

    C. V. Hollot

  2. Department of Mechanics, Peking University, Peking, People's Republic of China

    Huang Lin (Visiting Scholar)

Authors
  1. A. C. Bartlett
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  2. C. V. Hollot
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  3. Huang Lin
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Additional information

A. C. Bartlett was with the Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, New York. 12180, U.S.A. He is now with the Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, Massachusetts 01003, U.S.A.

The work of this author was supported by the National Science Foundation under Grant No. ECS-8609790.

The work of this author was supported by the Chinese Academy of Sciences and the State Education Commission of China.

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Bartlett, A.C., Hollot, C.V. & Lin, H. Root locations of an entire polytope of polynomials: It suffices to check the edges. Math. Control Signal Systems 1, 61–71 (1988). https://doi.org/10.1007/BF02551236

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  • DOI: https://doi.org/10.1007/BF02551236

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