Abstract
The families of spherical polynomials provide not very commonly utilized definition of uncertainty bounding set for systems with parametric uncertainty. The principal aim of this contribution is to present such spherical polynomial families, their description and related robust stability analysis. The illustrative example demonstrates an easy-to-use graphical method of robust stability investigation theoretically based on the value set concept and the zero exclusion condition and practically performed through the Polynomial Toolbox for Matlab.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barmish, B.R.: New Tools for Robustness of Linear Systems. Macmillan, New York (1994)
Tesi, A., Vicino, A., Villoresi, F.: Robust Stability of Spherical Plants with Unstructured Uncertainty. In: Proceedings of the American Control Conference, Seattle, Washington, USA (1995)
Polyak, B.T., Shcherbakov, P.S.: Random Spherical Uncertainty in Estimation and Robustness. In: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia (2000)
Chen, J., Niculescu, S.-I., Fu, P.: Robust Stability of Quasi-Polynomials: Frequency-Sweeping Conditions and Vertex Tests. IEEE Transactions on Automatic Control 53(5), 1219–1234 (2008)
Hurák, Z., Šebek, M.: New Tools for Spherical Uncertain Systems in Polynomial Toolbox for Matlab. In: Proceedings of the Technical Computing Prague 2000, Prague, Czech Republic (2000)
PolyX: The Polynomial Toolbox, http://www.polyx.com
Matušů, R.: Families of spherical polynomials: Description and robust stability analysis. In: Latest Trends on Systems (Volume II) – Proceedings of the 18th International Conference on Systems, Santorini, Greece, pp. 606–610 (2014)
Šebek, M.: Robustní řízení (Robust Control). PDF slides for course “Robust Control”, ČVUT Prague, http://dce.felk.cvut.cz/ror/prednasky_sebek.html or http://www.polyx.com/_robust/ (in Czech)
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)
Bhattacharyya, S.P., Chapellat, H., Keel, L.H.: Robust control: The parametric approach. Prentice Hall, Englewood Cliffs (1995)
Matušů, R., Prokop, R.: Graphical analysis of robust stability for systems with parametric uncertainty: an overview. Transactions of the Institute of Measurement and Control 33(2), 274–290 (2011)
Soh, C.B., Berger, C.S., Dabke, K.P.: On the stability properties of polynomials with perturbed coefficients. IEEE Transactions on Automatic Control 30(10), 1033–1036 (1985)
Barmish, B.R., Tempo, R.: On the spectral set for a family of polynomials. IEEE Transactions on Automatic Control 36(1), 111–115 (1991)
Biernacki, R.M., Hwang, H., Bhattacharyya, S.P.: Robust stability with structured real parameter perturbations. IEEE Transactions on Automatic Control 32(6), 495–506 (1987)
PolyX: The Polynomial Toolbox for Matlab – Upgrade Information for Version 2.5 (2001), http://www.polyx.com/download/OnLineUpgradeInfo25.pdf.gz
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Matušů, R., Prokop, R. (2015). Robust Stability Analysis for Families of Spherical Polynomials. In: Silhavy, R., Senkerik, R., Oplatkova, Z., Prokopova, Z., Silhavy, P. (eds) Intelligent Systems in Cybernetics and Automation Theory. CSOC 2015. Advances in Intelligent Systems and Computing, vol 348. Springer, Cham. https://doi.org/10.1007/978-3-319-18503-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-18503-3_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18502-6
Online ISBN: 978-3-319-18503-3
eBook Packages: EngineeringEngineering (R0)