Stabilization of Discrete System with Bounded Parameters

Year 2017, Volume: 18 Issue: 2, 500 - 506, 30.06.2017

Taner Büyükköroğlu , Vakif Dzhafarov

https://doi.org/10.18038/aubtda.299974

Abstract

In this paper stabilization problem of linear discrete single input, single output plant by affine stabilizator is considered. It is assumed that stabilizing vector is bounded and its values are changed in a given box. We use the Schur-Szegö parameters (reflection coefficients) and obtain conditions for nonexistence and existence of a stabilizing vector.

Keywords

Schur stability, Reflection coefficients, Stabilizing vector

References

• [1] Levinson N. The Wiener RMS error criterion in filter design and prediction. J. Math. Phys., vol. 25, no. 1–4, pp. 261–278, 1946.
• [2] Nurges Ü. New stability conditions via reflection coefficients of polynomials. IEEE Transactions on Automatic Control, vol. 50, no. 9, pp. 1354–1360, 2005.
• [3] Büyükköroğlu T. Fixed order controller for Schur stability. Math. Comput. Appl., vol. 21, no. 2, paper no. 25, pp.1-9, 2016.
• [4] Fam AT, Meditch JS. A canonical parameter space for linear systems design. IEEE Transactions on Automatic Control, vol. 23, no. 3, pp. 454–458, 1978.
• [5] Petrikevich YI. Randomized methods of stabilization of the discrete linear systems. Automation and Remote Control, vol. 69, no. 11, pp. 1911–1921, 2008.
• [6] Polyak BT, Shcherbakov PS. Hard problems in linear control theory: possible approaches to solution. Automation and Remote Control, vol. 65, no. 5, pp. 681–718, 2005.
• [7] Nurges Ü, Avanessov S. Fixed-order stabilising controller design by a mixed randomized/deterministic method. Int. J. Control, vol. 88, no. 2, pp. 335–346, 2015.
• [8] Büyükköroğlu T, Çelebi G, Dzhafarov V. Stabilization of discrete time systems by reflection coefficients. Tr. Inst. Math. Mekh. UrO RAN, vol. 23, no. 1, pp. 306–311, 2017.
• [9] Waqar AM, Swaroop D, Bhattacharyya SP. Synthesis of fixed structure controllers for discrete time systems. Numerical Linear Algebra in Signals, Systems and Control. Volume 80 of the series Lecture Notes in Electrical Engineering, pp 367-385, 2011.