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Stability Analysis of Multi-Dimensional Linear Discrete System and Root Distribution Using Sign Criterion with Real Coefficients
Department of Electrical and Electronics Engineering, Anna University, University College of Engineering, Ramanathapuram Campus, Ramanathapuram, India
- 1 Department of Electrical and Electronics Engineering, Anna University, University College of Engineering, Ramanathapuram Campus, Ramanathapuram, India
Circuits and Systems·Volume 07 (2016)·Pages 100–109·Published 23 March 2016·DOI10.4236/cs.2016.73010
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Abstract
A new idea was proposed to find out the stability and root location of multi-dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is synthesized from the Jury’s method for stability which is derived from the characteristic polynomial coefficients of the discrete system. The number of roots lying inside or outside the unit circle and hence on the unit circle is directly determined from the proposed single modified Jury tabulation and the sign criterion. The proposed scheme is simple and the examples are given to bring out the merits of the proposed scheme which is also applicable for the singular and non-singular cases.
KeywordsRoot DistributionInside the Unit CircleOutside the Unit CircleCharacteristics PolynomialMulti-Dimensional
- Jury, E.I. and Blanchard, J. (1961) A Stability Test for Linear Discrete Systems in Table Form. Proceedings of the IRE, 21, 1947-1948.
- De la sen, M. (2007) Stability Criteria for Linear Time Invariant Systems with Point Delays Based on One Dimensional Routh-Hurwitztests. Applied mathematics and computation, 187, 1199-1207.
- KarivarathaRajan, P. and Reddy, H.C. (1989) A Test Procedure for 2-D Discrete Scattering Hurwitz Polynomials. IEEE Transactions on Acoustics, Speech and Signal Processing, 37, 118-120. http://dx.doi.org/10.1109/29.17508
- Serban, I. and Najim, M. (2007) A New Multi-Dimensional Schur-Cohn Type Stability Criterion. IEEE Proceedings of the American Control Conference, New York, 9-13 July 2007, 5533-5538.
- Bistriz, Y. (2006) Critical stability Constraints for Discrete-Time Linear Systems. IEEE Transaction on Circuits and Systems II: Express Briefs, 53, 95-99. http://dx.doi.org/10.1109/TCSII.2005.856032
- Benidir, M. (1991) Sufficient Conditions for the Stability of Multidimensional Recursive Digital Filters. Proceedings of the International Conference on Acoustics, Speech and Signal Processing, Toronto, 14-17 April 1991, 2885-2888. http://dx.doi.org/10.1109/icassp.1991.151005
- Bose, N.K. and Jury, E.I. (1974) Positivity & Stability Tests for Multidimensional Filters (Discrete-Continuous). IEEE Transactions on Acoustics, Speech & Signal Processing, 22, 174-180. http://dx.doi.org/10.1109/TASSP.1974.1162564
- Bose, N.K. and Kamat, P.S. (1974) Algorithm for Stability Test of Multidimensional Filters. IEEE Transaction on Acoustics and Signal processing, 22, 307-314.
- Bose, N.K. and Modarressi, A.K. (1976) General Procedure for Multivariable Positivity Test with Control Applications. IEEE Transactions on Automatic Control, 21, 696-701. http://dx.doi.org/10.1109/TAC.1976.1101356
- Bose, N.K. and Zeheb, E. (1986) Kharitonov’s Theorem and Stability Test of Multidimensional Digital Filters. Proceedings of the IEE on Electronic Circuits and Systems, 133, 187-190. http://dx.doi.org/10.1049/ip-g-1.1986.0030
- Hertz, D. and Zeheb, E. (1984) Sufficient Conditions for Stability of Multidimensional Discrete Systems. Proceedings of the IEEE, 72, 226.
- Kurosawa, K., Yamada, I., Yokokawa, T. and Tsujii, S. (1993) A Fast Stability Test for Multidimensional Systems. IEEE International Symposium on Circuits and Systems, Tokyo Institute of Technology, Vol. 152, 579-582.