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A Matlab Program for Analysis of Robust Stability Under Parametric Uncertainty

  • Radek Matušů
  • Diego Piñeiro Prego
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 466)

Abstract

The main aim of this contribution is to present a Matlab program for robust stability analysis of families of polynomials with parametric uncertainty. The created software is applicable for basic uncertainty structures such as single parameter uncertainty (including quasi-polynomials), independent (interval) uncertainty structure, affine linear, multilinear, polynomial or general uncertainty structure. Moreover, the discrete-time interval polynomials can be analyzed as well. From the viewpoint of available tools, the program incorporates the Root Locus, the Bialas Eigenvalue Criterion, the Kharitonov Theorem, the Tsypkin-Polyak Theorem, the Edge Theorem and the Value Set Concept combined with the Zero Exclusion Condition. The use of the toolbox is briefly outlined by means of the simple example.

Keywords

Robust stability analysis Parametric uncertainty Matlab 

Notes

Acknowledgments

The work was supported by the Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme project No. LO1303 (MSMT-7778/2014). This assistance is very gratefully acknowledged.

References

  1. 1.
    Matušů, R., Prokop, R.: Robust stability analysis for families of spherical polynomials. In: Advances in Intelligent Systems and Computing, vol. 348. In: Proceedings of the 4th Computer Science On-line Conference 2015 (CSOC2015), vol. 2: Intelligent Systems in Cybernetics and Automation Theory, pp. 57–65. Springer International Publishing, Cham (2015)zbMATHGoogle Scholar
  2. 2.
    Barmish, B.R.: New Tools for Robustness of Linear Systems. Macmillan, New York (1994)zbMATHGoogle Scholar
  3. 3.
    Bhattacharyya, S.P., Chapellat, H., Keel, L.H.: Robust control: The Parametric Approach. Prentice Hall, Englewood Cliffs (1995)zbMATHGoogle Scholar
  4. 4.
    Prego, D.P.: A software program for graphical robust stability analysis. Student Project Report, Faculty of Applied Informatics, Tomas Bata University in Zlín, Czech Republic (2015)Google Scholar
  5. 5.
    Bialas, S.: A necessary and sufficient condition for the stability of convex combinations of stable polynomials or matrices. Bull. Polish Acad. Sci. Tech. Sci. 33, 473–480 (1985)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Kharitonov, V.L.: Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsial’nye Uravneniya 14, 2086–2088 (1978)Google Scholar
  7. 7.
    Tsypkin, Y.Z., Polyak, B.T.: Frequency domain criteria for lp-robust stability of continuous linear systems. IEEE Trans. Autom. Control 36(12), 1464–1469 (1991)CrossRefGoogle Scholar
  8. 8.
    Bartlett, A.C., Hollot, C.V., Huang, L.: Root locations of an entire polytope of polynomials: it suffices to check the edges. Math. Control Signals Syst. 1, 61–71 (1988)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Matušů, R., Prokop, R.: Graphical analysis of robust stability for systems with parametric uncertainty: an overview. Trans. Inst. Meas. Control 33(2), 274–290 (2011)CrossRefGoogle Scholar
  10. 10.
    Matušů, R., Prokop, R.: Robust stability analysis for systems with real parametric uncertainty: implementation of graphical tests in Matlab. Int. J. Circuits Syst. Signal Process. 7(1), 26–33 (2013)Google Scholar
  11. 11.
    Matušů, R.: Robust stability analysis of discrete-time systems with parametric uncertainty: a graphical approach. Int. J. Math. Models Methods Appl. Sci. 8, 95–102 (2014)Google Scholar

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© Springer International Publishing Switzerland 2016

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Authors and Affiliations

  1. 1.Information and Advanced Technologies (CEBIA—Tech), Faculty of Applied InformaticsTomas Bata University in ZlínZlínCzech Republic

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