Abstract
The contribution focuses on the value sets of the ellipsoidal polynomial families with affine linear uncertainty structure. First, it recalls the fundamental terms from the area of robustness under parametric uncertainty, such as uncertainty structure, uncertainty bounding set, family, and value set, with emphasis to the ellipsoidal polynomial families. Then, the illustrative example is elaborated, in which the value sets of the ellipsoidal polynomial family with affine linear uncertainty structure are plotted, including randomly chosen internal points, and compared with the value sets of the classical “box” version of the polynomial family.
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
Similar content being viewed by others
References
Barmish, B.R.: New Tools for Robustness of Linear Systems. Macmillan, New York (1994)
Bhattacharyya, S.P.: Robust control under parametric uncertainty: an overview and recent results. Annu. Rev. Control 44, 45–77 (2017)
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)
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)
Matušů, R., Pekař, R.: Robust stability of thermal control systems with uncertain parameters: the graphical analysis examples. Appl. Therm. Eng. 125, 1157–1163 (2017)
Matušů, R., Prokop, R.: Robust stability analysis for families of spherical polynomials. In: Intelligent Systems in Cybernetics and Automation Theory. Proceedings of CSOC 2015. Advances in Intelligent Systems and Computing, vol. 348, pp. 57–65. Springer, Cham (2015)
Matušů, R.: Spherical families of polynomials: a graphical approach to robust stability analysis. Int. J. Circuits Syst. Signal Process. 10, 326–332 (2016)
Hurák, Z., Šebek, M.: New tools for spherical uncertain systems in polynomial toolbox for Matlab. In: Proceedings of the Technical Computing Prague, Prague, Czech Republic (2000)
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 Trans. Autom. Control 53(5), 1219–1234 (2008)
Soh, C.B., Berger, C.S., Dabke, K.P.: On the stability properties of polynomials with perturbed coefficients. IEEE Trans. Autom. Control 30(10), 1033–1036 (1985)
Barmish, B.R., Tempo, R.: On the spectral set for a family of polynomials. IEEE Trans. Autom. Control 36(1), 111–115 (1991)
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)
Biernacki, R.M., Hwang, H., Bhattacharyya, S.P.: Robust stability with structured real parameter perturbations. IEEE Trans. Autom. Control 32(6), 495–506 (1987)
Sadeghzadeh, A., Momeni, H.: Fixed-order robust H∞ control and control-oriented uncertainty set shaping for systems with ellipsoidal parametric uncertainty. Int. J. Robust Nonlinear Control 21(6), 648–665 (2011)
Sadeghzadeh, A., Momeni, H., Karimi, A.: Fixed-order H∞ controller design for systems with ellipsoidal parametric uncertainty. Int. J. Control 84(1), 57–65 (2011)
Sadeghzadeh, A., Momeni, H.: Robust output feedback control for discrete-time systems with ellipsoidal uncertainty. IMA J. Math. Control Inf. 33(4), 911–932 (2016)
Acknowledgments
This 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).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Matušů, R. (2019). Value Sets of Ellipsoidal Polynomial Families with Affine Linear Uncertainty Structure. In: Silhavy, R. (eds) Cybernetics and Automation Control Theory Methods in Intelligent Algorithms. CSOC 2019. Advances in Intelligent Systems and Computing, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-19813-8_26
Download citation
DOI: https://doi.org/10.1007/978-3-030-19813-8_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-19812-1
Online ISBN: 978-3-030-19813-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)