Skip to main content
Log in

Strict Hurwitzness of Bivariate Polynomials Under Polynomial Perturbations

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

The paper concerns strict Hurwitzness of interval bivariatepolynomials under a family of interval polynomial perturbations.Necessary and sufficient strict Hurwitzness conditions are derived.We define the stability radius r for polynomialperturbations, and provide a formula for r.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. K. Bose, Applied Multidimensional Systems Theory, Van Nostrand Reinhold, 1982.

  2. N. K. Bose, “Robust Multivariable Scattering Hurwitz Interval Polynomials,” Linear Algebra and Its Applications, vol. 98, 1988, pp. 123–136.

    Google Scholar 

  3. B. G. Il’yasov and Yu. S. Kabal’nov, “An Investigation into the Stability of Single–Type Multiply Connected Automatic Control Systems with Holonomic Ties Between Subsystems,” Automation and Remote Control, vol. 56, no. 8, 1995, pp. 1120–1125.

    Google Scholar 

  4. V. L. Kharitonov, “Robust Stability of Nested Polynomial Families,” Automatica, vol. 32, no. 3, 1996, pp. 365–367.

    Google Scholar 

  5. V. L. Kharitonov, “Stability of Nested Polynomial Families,” Automation and Remote Control, in press.

  6. K. D. Kim and N. K. Bose, “Invariance of the Strict Hurwitz Property for Bivariate Polynomials Under Coefficient Perturbations,” IEEE Trans. Autom. Contr., vol. AC-33, no. 12, 1988, pp. 1172–1174.

    Google Scholar 

  7. J. Kogan, “Computation of Stability Radius for Families of Bivariate Polynomials,” Multidimensional Systems and Signal Processing, vol. 4, 1993, pp. 151–165.

    Google Scholar 

  8. J. Kogan, “Robust Stability and Convexity: An Introduction,” Lecture Notes in Control and Information Sciences No. 201, London: Springer-Verlag, 1995.

    Google Scholar 

  9. A. A. Krasovskii, “On Automatic Control Processes of Single–Type Interconnected Linear Systems,” Zhykovskii VVIA, vol. 576, 1955 (in Russian).

  10. T. Mori and H. Kokame, “An Extension of Kharitonov's Theorem and its Applications,” Proceedings of the American Control Conference, Atlanta, 1988, pp. 892–896.

  11. B. T. Polyak and S. B. Shmulyian, “Frequency Domain Criteria for Robust Stability of Bivariate Polynomials,” IEEE Trans. Circuits Syst., vol. CAS-41, no. 2, 1994, pp. 161–167.

    Google Scholar 

  12. B. T. Polyak and Ya. Z. Tsypkin, “Stability and Robust Stability of Single–Type Systems,” Automation and Remote Control, to appear.

  13. A. Rantzer, “Kharitonov's Weak Theorem Holds If and Only If the Stability Region and Its Reciprocal are Convex,” Int. J. of Nonlinear and Robust Contr., vol. 3, 1993, pp. 55–62.

    Google Scholar 

  14. O. S. Sobolev, Single–Type Connected Regulation Systems, Moscow: Energiya, 1973 (in Russian).

    Google Scholar 

  15. E. Walach and E. Zeheb, “Generalized Zero Sets of Multiparameter Polynomials and Feedback Stabilization,” IEEE Trans. on Circ. and Syst., vol. 29, no. 1, 1982, pp. 15–23.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kogan, J. Strict Hurwitzness of Bivariate Polynomials Under Polynomial Perturbations. Multidimensional Systems and Signal Processing 8, 469–479 (1997). https://doi.org/10.1023/A:1008264526105

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008264526105

Navigation