New Trends in Systems Theory pp 42-49 | Cite as
New Results in the Stability Analysis of Two-Dimensional Systems
Chapter
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.
Keywords
Characteristic Polynomial Lyapunov Equation Multidimensional System Hermitian Solution Positive Definite Solution
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- [1]Jury, E.I., “Stability of Multidimensional Systems and Related Problems”, in Multidimensional Systems, ed. by S. Tzafestas, Marcel Dekker, pp. 89–159, 1986.Google Scholar
- [2]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.Google Scholar
- [3]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.Google Scholar
- [4]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.Google Scholar
- [5]Fornasini, E., and G. Marchesini, “Stability Analysis of 2-D Systems”, IEEE Trans. Circuits Syst., vol. CAS-27, pp. 1210–1217, Dec. 1980.Google Scholar
- [6]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.Google Scholar
- [7]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.Google Scholar
- [8]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.Google Scholar
- 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.Google Scholar
- [10]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.Google Scholar
- [11]Sendaula, M., “A 2-D Algebraic Stability Test”, inProc. of the IEE ISCAS 1988, Helsinki, Finland, pp. 393–396, June 1988.Google Scholar
- [12]Gutwan, S., “State-Space Stability of Two-Dimensional Systems”, IMA Journal of Mathematical Control & Information, vol. 4, pp. 55–63, 1987.CrossRefGoogle Scholar
- [13]Fernando, K.V., “Stability of 2D State-Space Systems”, NAG Technical Report TR4/88, 1988.Google Scholar
- [14]Roesser, R.P., “A Discrete State-Space Model for Linear Image Processing”, IEEE Trans, on AC, vol. AC-20, pp. 1–10, 1975.Google Scholar
- [15]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.Google Scholar
- [16]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.Google Scholar
- [17]Anderson, B.D.O. and S. Vongpanitlerd, “Network Analysis and Synthesis; A Modern System Theory Approach”, Prentice Hall, New Jersey, 1973.Google Scholar
- [18]Vidyanathan P.P., “Discrete-Time Bounded Real Lemma in Digital Filtering”, IEEE Trans on CAS, Vol CAS-32, pp. 918–924, 1985.Google Scholar
Copyright information
© Springer Science+Business Media New York 1991