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Optimum Radius of Robust Stability for Schur Polynomials

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Abstract

The paper investigates the problem of the robust stability of Schur polynomials. Recently, a new approach based on the Rouche theorem of classical complex analysis has been adopted for the solution of this problem. In this paper, an improvement of the previous solution is presented. This is the optimum solution of the robust stability problem for Schur polynomials, which is obtained by solving a minimization problem and is better than other methods in robust stability literature. Three numerical examples are given to illustrate the proposed method.

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References

  1. Kharitonov, V. L., Asymptotic Stability of an Equilibrium Position of a Family of Systems of Linear Differential Equations, Differential Equations, Vol. 14, pp. 1483–1485, 1979.

    Google Scholar 

  2. Chapellat, H., and Bhattacharyya, S. P., An Alternative Proof of Kharitonov's Theorem, IEEE Transactions on Automatic Control, Vol. 34, No. 4, pp. 448–450, 1989.

    Google Scholar 

  3. Minnichelli, R. J., Anagnost, J. J., and Desoer, C. A., An Elementary Proof of Kharitonov'sStability Theorem, IEEE Transactions on Automatic Control, Vol. 34, No. 9, pp. 995–998, 1989.

    Google Scholar 

  4. Tempo, R., A Dual Result to Kharitonov'sTheorem, IEEE Transactions on Automatic Control, Vol. 35, No. 2, pp. 195–198, 1990.

    Google Scholar 

  5. Xu, S. J., Darouach, M., and Schaefers, J., Expansion of det(ACB) and Robustness Analysis of Uncertain StateSpace Systems, IEEE Transactions on Automatic Control, Vol. 38, No. 11, pp. 1671–1675, 1993.

    Google Scholar 

  6. Katbab, A., and Jury, E., On the Strictly-Positive Realness of Schur Interval Functions, IEEE Transactions on Automatic Control, Vol. 35, No. 12, pp. 1382–1385, 1989.

    Google Scholar 

  7. Xu, S. J., Rachid, A., and Darouach, M., Robustness Analysis of Interval Matrices Based on Kharitonov'sTheorem, IEEE Transactions on Automatic Control, Vol. 43, No. 2, pp. 273–277, 1998.

    Google Scholar 

  8. Barmish, B. R., New Tools for Robustness of Linear Systems, Macmillan Publishing Company, New York, NY, 1994.

    Google Scholar 

  9. Soh, Y. C., Xie, L., and Foo, Y. K., Maximal Perturbation Bound for Perturbed Polynomials with Roots in the Left Sector, IEEE Transactions on Circuits and Systems, Part 1, Vol. 41, No. 4, pp. 281–285, 1994.

    Google Scholar 

  10. Soh, C. B., Robust Stability of Discrete-Time Systems Using Delta Operators, IEEE Transactions on Automatic Control, Vol. 36, No. 3, pp. 377–380, 1991.

    Google Scholar 

  11. Mastorakis, N. E., Robust Stability of Polynomials: A New Approach, Journal of Optimization Theory and Applications, Vol. 93, No. 3, pp. 635–638, 1997.

    Google Scholar 

  12. Caratheodory, C., Theory of Functions of a Complex Variable, Chelsea Publishing Company, New York, NY, 1964.

    Google Scholar 

  13. Luenberger, D. G., Introduction to Linear and Nonlinear Programming, Addison-Wesley Publishing Company, Reading, Massachusetts, 1973.

    Google Scholar 

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Mastorakis, N.E. Optimum Radius of Robust Stability for Schur Polynomials. Journal of Optimization Theory and Applications 104, 165–174 (2000). https://doi.org/10.1023/A:1004684907724

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