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Convex combinations of G-stable polynomials

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Abstract

Two methods are proposed to evaluate G-stability of a convex combination of two G-stable polynomials.

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References

  • S.P. Bhattacharyya,Robust Stabilization against Structured Perturbations, Springer Verlag, Lecture Notes in Control and Information Sciences, vol. 99, 1987.

  • H. Chapellat and S.P. Bhattacharyya, “An Alternative Proof of the Kharitonov Theorem,”IEEE Trans. Automatic Control, vol. 34, pp. 448–450, April, 1989.

    Article  Google Scholar 

  • B.R. Barmish, “A Generalization of the Kharitonov's Four Polynomial Concept for Robust Stability Problems with Linearly Dependent Coefficient Perturbations,”IEEE Trans. Automatic Control, vol. 34, pp. 157–165, February, 1989.

    Article  Google Scholar 

  • N.K. Bose and Y.Q. Shi, “A Simple General Proof of Kharitonov's Generalized Stability Criteria,”IEEE Trans. Circuits and Systems, vol. CAS-34, pp. 1233–1237, March, 1989.

    Google Scholar 

  • H. Chapellat and S.P. Bhattacharyya, “A Generalization of Kharitonov's Theorem: Robust Stability of Interval Plants,”IEEE Trans. Automatic Control, vol. 34, pp. 306–311, March, 1989.

    Article  Google Scholar 

  • A.G. Bartlett, C.V. Hollot, et al., “Root Location of an Entire Polytope of Polynomials: It Suffices to Check the Edges,”Mathematics of Control, Signals and Systems, vol. 1, pp. 61–71, 1988.

    Google Scholar 

  • C.V. Hollot, D.P. Looze, et al., “Parametric Uncertainty and Unmodeled Dynamics: Analysis via Parameter Space Methods,”Automatica, vol. 26, pp. 269–282, March, 1990.

    Article  MathSciNet  Google Scholar 

  • B.R. Barmish and Z. Shi, “Robust Stability of Perturbed Systems with Time Delays,”Automatica, vol. 25, pp. 371–381, March, 1989.

    Article  Google Scholar 

  • B.R. Barmish and R. Tempo, “The Robust Root Locus,”Automatica, vol. 26, pp. 283–292, March, 1990.

    Article  Google Scholar 

  • M. Fu, A.W. Olbrot, et al., “Introduction to the Parametric Approach to Robust Stability,”IEEE Control System Magazine, pp. 7–11, August, 1989.

  • D.D. Siljak, “Parameter Space Methods for Robust Control Design: A Guided Tour,”IEEE Trans. Automatic Control, vol. 34, pp. 674–688, July, 1989.

    Article  Google Scholar 

  • R.T. Rockefellar,Conex Analysis, Princeton, NJ: Princeton University Press, 1970.

    Google Scholar 

  • H. Taub and S. Gutman, “A Symmetric Matrix Criterion for Polynomial Root Clustering,”IEEE Trans. Circuits and Systems, vol. 37, pp. 243–248, February, 1990.

    Article  Google Scholar 

  • K.P. Sondergeld, “A Generalization of the Routh-Hurwitz Stability Criteria and an Application to a Problem in Robust Controller Design,”IEEE Trans. Automatic Control, vol. AC-28, pp. 965–970, October, 1983.

    Article  Google Scholar 

  • M. Fu and B.R. Barmish, “Stability of Conve and Linear Combinations of Polynomials and Matrices Arising in Robustness Problems,”Proceedings of the 1987 Conference on Information Sciences and Systems, John Hopkins University, Baltimore, Marland, pp. 16–21, 1987.

    Google Scholar 

  • S. Bialas and J. Garloff, “Convex Combinations of Stable Polynomials,”Journal of the Franklin Institute, vol. 319, no. 3, pp. 373–377, 1985.

    Article  Google Scholar 

  • N.K. Bose, “Tests for Hurwitz and Schur Properties of Convex Combination of Complex Polynomials,”IEEE Trans. Circuits and Systems, vol. 36, pp. 1245–1247, September, 1989.

    Article  Google Scholar 

  • F.R. Gantmacher,The Theory of Matrices, vol. II, Chelsea, NY, 1977.

  • J.E. Ackerman and B.R. Barmish, “Robust Schur Stability of a Polytope of Polynomials,”IEEE Trans. Automatic Control, vol. 33, pp. 984–986, October, 1988.

    Article  Google Scholar 

  • E.I. Jury,Inners and Stability of Dynamic Systems, New York: Wiley, 1974; also Krieger, FL, 1982.

    Google Scholar 

  • D.D. Siljak,Nonlinear Systems, The Parameter Analysis and Design, Wiley, 1968.

  • J.N. Franklin,Matrix Theory, Englewood Cliffs, NJ: Prentice Hall, 1966.

    Google Scholar 

  • M. Fu and B.R. Barmish, “Polytopes of Polynomials with Zeros in a Prescribed Set,”IEEE Trans. Automatic Control, vol. 34, pp. 544–546, May, 1989.

    Article  Google Scholar 

  • S. Bialas, “A Necessary and Sufficient Condition for the Stability of Convex Combinations of Stable Polynomials or Matrices,”Bull. of the Polish Academy of Science, vol. 33, pp. 473–480, 1985.

    Google Scholar 

  • H. Boguerra, B.S. Chang, et al., “Fast Stability Checking for the Convex Combination of Stable Polynomials,”IEEE Trans. Automatic Control, vol. AC-35, pp. 586–588, May, 1990.

    Article  Google Scholar 

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Author notes

  1. Marek K. Solak

    Present address: Institute of Electrical Engineering, ul. Pożaryskiego 28, 04-703, Warsaw, Poland

Authors and Affiliations

  1. Department of Electrical and Control Engineering, University of Durban-Westville, Private Bag X54001, 4000, Durban, South Africa

    Marek K. Solak

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  1. Marek K. Solak
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Solak, M.K. Convex combinations of G-stable polynomials. Multidim Syst Sign Process 2, 337–343 (1991). https://doi.org/10.1007/BF01952239

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  • DOI: https://doi.org/10.1007/BF01952239

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