Abstract
The extension of the Lyapunov equation to the two- and multi-dimensional systems is an important problem in the stability analysis and implementation of such systems. In this paper a brief review of results in this areas is given and the relationships between the various approaches are discussed.
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
Preview
Unable to display preview. Download preview PDF.
References
Jury, E.I., “Stability of Multidimensional Systems and Related Problems”, in Multidimensional Systems, ed. by S. Tzafestas, Marcel Dekker, pp. 89–159, 1986.
Piekarski, M.S., “Algebraic Characterization of Matrices Whose Multivariable Characteristic polynomial is Hurwitzian”, in Proc. Int. Symp. Operator Theory, Lubbock, TX, pp. 121–126, Aug. 1977.
Anderson, B.D.O., P. Agathoklis, E.I. Jury and M. Mansour, “Stability and the Matrix Lyapunov Equation for Discrete 2-Dimensional Systems”, IEEE Trans, on CAS, pp. 261–267, Mar. 1986.
Agathoklis, P., E.I. Jury and M. Mansour, “The Discrete-Time Strictly Bounded-Real Lemma and the Computation of Positive Definite Solutions to the 2-D Lyapunov Equation”, IEEE Trans, on CAS, vol. 36, pp. 830–837, 1989.
Fornasini, E., and G. Marchesini, “Stability Analysis of 2-D Systems”, IEEE Trans. Circuits Syst., vol. CAS-27, pp. 1210–1217, Dec. 1980.
Lu, W.-S., and E.B. Lee, “Stability Analysis for Two-dimensional Systems Via a Lyapunov Approach”, IEEE Trans, on Circuits Syst., vol. CAS-32, pp. 61–68, Jan. 1985.
Agathoklis, P., “On the Very Strict Hurwitz Property of the 2-D Characteristic Polynomial of a Matrix”, Proc. of IEEE Int. Con), on ASSP 88, New York, pp. 856–859, April 1988.
Agathoklis, P., “Conditions for the 2-D Characteristic Polynomial of a Matrix to be Very Strict Hurwitz”, IEEE Trans, on ASSP, vol. ASSP-37, pp. 1284–1286,1989.
Agathoklis, P. and S. Foda, “Stability and the Matrix Lyapunov Equation for Delay-Differential Systems”, Int. J. of Control, vol. 49, No. 2, pp. 417–432.
Basu, S., “On State-Space Formulation of Scattering Shur Property of Two-Dimensional Polynomials”, Proceedings of 1989 IEEE ISCAS, Portland, Oregon,pp. 1491–1494, May 8–11, 1989.
Sendaula, M., “A 2-D Algebraic Stability Test”, inProc. of the IEE ISCAS 1988, Helsinki, Finland, pp. 393–396, June 1988.
Gutwan, S., “State-Space Stability of Two-Dimensional Systems”, IMA Journal of Mathematical Control & Information, vol. 4, pp. 55–63, 1987.
Fernando, K.V., “Stability of 2D State-Space Systems”, NAG Technical Report TR4/88, 1988.
Roesser, R.P., “A Discrete State-Space Model for Linear Image Processing”, IEEE Trans, on AC, vol. AC-20, pp. 1–10, 1975.
Agathoklis, P., E.I. Jury and M. Mansour, “An Algebraic Test for Internal Stability of 2-d Discrete Systems”, to be published in the Proceedings of the International Symposium MTNS 89, Progress in Systems and Control Series, Birkhaenser, Boston, 1990.
Agathoklis, P., E.I. Jury and M. Mansour, “Algebraic Necessary and Sufficient Conditions for the Very Strict Hurwitz Property of a 2-D Polynomial”, ted for publication in the Multidimensional Systems and Signal Processing Journal, 1990.
Anderson, B.D.O. and S. Vongpanitlerd, “Network Analysis and Synthesis; A Modern System Theory Approach”, Prentice Hall, New Jersey, 1973.
Vidyanathan P.P., “Discrete-Time Bounded Real Lemma in Digital Filtering”, IEEE Trans on CAS, Vol CAS-32, pp. 918–924, 1985.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Agathoklis, P. (1991). New Results in the Stability Analysis of Two-Dimensional Systems. In: New Trends in Systems Theory. Progress in Systems and Control Theory, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0439-8_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0439-8_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6760-7
Online ISBN: 978-1-4612-0439-8
eBook Packages: Springer Book Archive