Abstract
A method for constructing the interval stability set of a polynomial with interval coefficients polynomially depending on two parameters is proposed. The method is based on approximating the interval stability set with a given accuracy by a union of rectangles and does not require analyzing and constructing the boundaries of the D-decomposition. The convergence of the method is proved. The efficiency of the method is illustrated by examples.
Similar content being viewed by others
REFERENCES
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Metody klassicheskoi i sovremennoi teorii avtomaticheskogo upravleniya (Methods of Classical and Modern Automatic Control Theory), Pupkov, K.A., Ed., Moscow: Izd. MGTU im. N.E. Baumana, 2004, vol. 3.
Teoriya avtomaticheskogo upravleniya (Automatic Control Theory), Moscow: Vyssh. Shkola, 2005.
Rotach, V.Ya., Teoriya avtomaticheskogo upravleniya (Automatic Control Theory), Moscow: MEI, 2008.
Polyak, B.T., Khlebnikov, M.V., and Rapoport, L.B., Matematicheskaya teoriya avtomaticheskogo upravleniya (Mathematical Automatic Control Theory), Moscow: URSS, 2019.
Omorov, R.O., Algebraic method for studying the robustness of interval dynamical systems, Nauchno-Tekh. Vestn. Inf. Tekhnol. Mekh. Opt., 2020, vol. 20, no. 3, pp. 364–370.
Kim, D.P., Teoriya avtomaticheskogo upravleniya. Lineinye sistemy (Automatic Control Theory. Linear Systems), Moscow: Yurait, 2021.
Gu Da-Wei, Petko, Hr.P., and Konstantinov, M.M., Robust Control Design with Matlab, London: Springer, 2005.
Lin, F., Robust Control Design. An Optimal Control Approach, Chichester: John Wiley & Sons, 2007.
Sinha, A.K., Linear Systems. Optimal and Robust Control, Boca Raton: CRC Press, 2007.
Belmiloudi, A., Stabilization, Optimal and Robust Control: Theory and Applications in Biological and Physical Sciences, London: Springer, 2008.
Bartoszewicz, A., Robust Control, Theory and Applications, Rijeka, Croatia: InTech, 2011.
Levine, W.S., The Control Systems Handbook. Control System Advanced Methods, Boca Raton: CRC Press, 2011.
Yedavalli, R.K., Robust Control of Uncertain Dynamic Systems. A Linear State Space Approach, New York: Springer, 2014.
Dodds, S.J., Feedback Control. Linear, Nonlinear and Robust Techniques and Design with Industrial Applications, London: Springer, 2015.
Liu, K.-Z. and Yao, Y., Robust Control. Theory and Applications, Singapore: John Wiley & Sons, 2016.
Feng, Y. and Yagoubi, M., Robust Control of Linear Descriptor Systems, Singapore: Springer, 2017.
Garcia-Sanz, M., Robust Control Engineering. Practical QFT solutions, Boca Raton: CRC Press, 2017.
Golnarachi, F. and Kuo, B., Automatic Control Systems, New York: McGraw-Hill, 2017.
Franklin, G.F., Powell, J.D., and Emami-Naeini, A., Feedback Control of Dynamic Systems, London: Pearson Educ., 2020.
Astrom, K.J. and Murray, R.M., Feedback Systems: An Introduction for Scientists and Engineers, Princeton: Princeton Univ. Press, 2021.
Baillieul, J. and Samad, T., Encyclopedia of Systems and Control, London: Springer, 2021.
Dorf, R. and Bishop, R., Modern Control Systems, London: Pearson Educ., 2022.
Fortuna, L., Frasca, M., and Buscarino, A., Optimal and Robust Control Advanced Topics with MATLAB, Boca Raton: CRC Press, 2022.
Petrov, N.P. and Polyak, B.T., Robust D-decomposition, Autom. Remote Control, 1991, vol. 52, no. 11, pp. 1513–1523.
Neimark, Yu.I., Ustoichivost’ linearizovannykh sistem (Stability of Linearized Systems), Leningrad: LKVVIA, 1949.
Neimark, Yu.I., Dinamicheskie sistemy i upravlyaemye protsessy (Dynamic Systems and Controlled Processes), Moscow: Nauka, 1978.
Kharitonov, V.L., On the asymptotic stability of the equilibrium position of a family of systems of linear differential equations, Differ. Uravn., 1978, vol. 14, no. 11, pp. 2086–2088.
Polyak, B.T. and Tsypkin, Ya.Z., Frequency domain criteria for robust stability and aperiodicity of linear systems, Autom. Remote Control, 1990, vol. 51, no. 9, pp. 1192–1201.
Pryashnikova, P.F., D-decomposition in the case of polynomial dependence of the coefficients of a polynomial on two parameters, Autom. Remote Control, 2021, vol. 82, no. 3, pp. 398–409.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by V. Potapchouck
Rights and permissions
About this article
Cite this article
Pryashnikova, P.F. Robust D-Decomposition for a Polynomial Dependence of the Coefficients of a Polynomial on Two Parameters. Autom Remote Control 83, 1078–1092 (2022). https://doi.org/10.1134/S0005117922070050
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117922070050