CS  Vol.7 No.6 , May 2016
Certain Algebraic Test for Analyzing Aperiodic Stability of Two-Dimensional Linear Discrete Systems
Author(s) P. Ramesh
ABSTRACT
This paper addresses the new algebraic test to check the aperiodic stability of two dimensional linear time invariant discrete systems. Initially, the two dimensional characteristics equations are converted into equivalent one-dimensional equation. Further Fuller’s idea is applied on the equivalent one-dimensional characteristics equation. Then using the co-efficient of the characteristics equation, the routh table is formed to ascertain the aperiodic stability of the given two-dimensional linear discrete system. The illustrations were presented to show the applicability of the proposed technique.

Cite this paper
Ramesh, P. (2016) Certain Algebraic Test for Analyzing Aperiodic Stability of Two-Dimensional Linear Discrete Systems. Circuits and Systems, 7, 718-725. doi: 10.4236/cs.2016.76061.
References
[1]   Jury, E.I. and Gutman, S. (1975) On the Stability of the A Matrix inside the Unit Circle. IEEE Transaction on Automatic Control, 533-535.
http://dx.doi.org/10.1109/TAC.1975.1100995

[2]   Bistriz, Y. (2004) Immitance and Telepolation-Based Procedures to Test Stability of Continuous-Discrete Bivariate Polynomials. IEEE Transaction on Circuits and Systems, 3, 293-296.

[3]   Bistritz, Y. (2004) Testing Stability of 2-D Discrete Systems by a Set of Real 1-D Stability Tests. IEEE Transactions on Circuits and Systems I: Regular Papers, 51, 1312-1320.
http://dx.doi.org/10.1109/TCSI.2004.830679

[4]   Khargoneker, P.P. and Bruce Lee, E. (1986) Further Results on Possible Root Locations of 2-D Polynomials. IEEE Transactions on Circuits & Systems, 33, 566-569.
http://dx.doi.org/10.1109/TCS.1986.1085944

[5]   Mastorakis, N.E. (1998) A Method for Computing the 2-DStability Margin. IEEE Transactions on Circuits & Systems-II, Analog & Digital Signal Processing, 45, 376-378.
http://dx.doi.org/10.1109/82.664243

[6]   Anderson, B.D.O. and Jury, E.I. (1973) A Simplified Schur-Cohn Test. IEEE Transactions on Automatic Control, AU-31, 157-163.
http://dx.doi.org/10.1109/TAC.1973.1100253

[7]   Anderson, B.D.O. and Jury, E.I. (1973) Stability Test for Two-Dimensional Recursive Filter. IEEE Transactions on Audio Electroacoustics, AU-21, 366-372.
http://dx.doi.org/10.1109/TAU.1973.1162491

[8]   Jury, E.I. and Bauer, P. (1988) On the Stability of Two-Dimensional Continuous Systems. IEEE Transactions on Circuits and Systems, 35, 1487-1500.
http://dx.doi.org/10.1109/31.9912

[9]   Bose, N.K. and Jury, E.I. (1975) Inner Algorithm to Test for Positive Definiteness of Arbitrary Binary Forms. IEEE Transaction on Automatic Control, 169-170.
http://dx.doi.org/10.1109/TAC.1975.1100875

[10]   Jury, E.I. (1971) Inners-Approach to Some Problems of System Theory. IEEE Transactions on Automatic Control, AC-16, 233-240. http://dx.doi.org/10.1109/TAC.1971.1099725

[11]   Bistritz, Y. (2001) Stability Testing of 2-D Discrete Linear Systems by Telepolation of an Immittance-Type Tabular Test. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48, 840-846.
http://dx.doi.org/10.1109/81.933325

[12]   Ahmed, A. (1980) On the Stability of Two-Dimensional Discrete Systems. IEEE Transactions on Automatic Control, 25, 551-552. http://dx.doi.org/10.1109/TAC.1980.1102352

[13]   Jury, E.I. (1970) A Note on the Analytical Absolute Stability Test. Proceeding of the IEEE, 58, 823-824.
http://dx.doi.org/10.1109/PROC.1970.7763

[14]   Goodman, D. (1977) Some Stability Properties of Two-Dimensional Linear Shift-Invariant Digital Filters. IEEE Transactions on Circuits and Systems, 24, 201-208. http://dx.doi.org/10.1109/TCS.1977.1084322

[15]   Huang, T.S. (1972) Stability of Two-Dimensional Recursive Filters. IEEE Transactions on Audio and Electroacoustics, 20, 158-163.
http://dx.doi.org/10.1109/TAU.1972.1162364

[16]   Bauer, P. and Jury, E.I. (1988) Stability Analysis of Multidimensional (m-D) Direct Realization Digital Filters under the Influence of Nonlinearities. IEEE Transactions on Acoustics, Speech & Signal Processing, 36, 1770-1780.
http://dx.doi.org/10.1109/29.9014

[17]   Singh, V. (2012) New Approach to Stability of 2-D Discrete Systems with State Saturation. Signal Processing, 92, 240-247.
http://dx.doi.org/10.1016/j.sigpro.2011.07.012

[18]   Katbab, A., Jury, E.I. and Mansour, M. (1992) On Robust Schur Property of Discrete-Time Polynomials. IEEE Transactions on Circuits Systems I: Fundamental Theory and Applications, 39, 467-470.
http://dx.doi.org/10.1109/81.153641

[19]   Kamat, P.S. and Zwass, M. (1985) On Zero Location with Respect to the Unit Circle of Discrete-Time Linear Systems Polynomials. Proceedings of the IEEE, 73, 1686-1687.
http://dx.doi.org/10.1109/proc.1985.13351

[20]   Szaraniec, E. (1973) Stability, Instability and Aperiodicity Test for Linear Discrete Systems. Automatica, 9, 513-516.
http://dx.doi.org/10.1016/0005-1098(73)90097-6

[21]   Fuller, A.T. (1955) Conditions for Aperiodicity in Linear Systems. British Journal of Applied Physics, 5, 174-179.
http://dx.doi.org/10.1088/0508-3443/5/5/304

[22]   Jury, E.I. (1985) A Note on Aperiodicity Condition for Linear Discrete Systems. IEEE Transactions on Automatic Control, 30, 1100-1101.
http://dx.doi.org/10.1109/tac.1985.1103843

[23]   Jury, E.I. and Blanchard, J. (1961) A Stability Test for Linear Discrete Systems in Table Form. Proceedings of the IRE, 21, 1947-1948.

[24]   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

[25]   Jury, E.I. (1988) Modified Stability Table for 2-D Digital Filters. IEEE Transactions on Circuits and Systems, 35, 116- 119.
http://dx.doi.org/10.1109/31.1707

 
 
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