Abstract
Stability of a system described by the time-varying nonlinear 2-D Fornasini-Marchesini model is considered. There are given notions of stability of the system and theorems for stability and asymptotic stability which can be considered as the Lyapunov stability theorem extension for the system.
Article PDF
References
Bliman P.-A. (2002) Lyapunov equation for the stability of 2-D systems. Multidimensional Systems and Signal Processing 13: 201–222
El-Agizi N. G., Fahmy M. M. (1979) Two-dimensional digital filters with no overflow oscillations. IEEE Transactions on Acoustics, Speech and Signal Processing ASSP-27: 465–469
Fornasini E., Marchesini G. (1980) Stability analysis of 2-D systems. IEEE Transactions on Circuits and Systems 27: 1210–1217
Kojima C., Rapisarda P., Takaba K. (2011) Lyapunov stability analysis of higher-order 2D systems. Multidimensional Systems and Signal Processing 22(4): 287–302
Kurek J. E. (1985) The general state-space model for 2-dimensional linear digital systems. IEEE Transactions on Automatic Control AC-30: 600–602
Kurek J. E. (1995) Stability of nonlinear parameter-varying digital 2-D systems. IEEE Transactions on Automatic Control 40: 1428–1432
Ogata K. (1967) State space analysis of control systems. Prentice-Hall, Inc., Englewood Cliffs
Roesser R. (1975) A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control AC-20: 1–10
Tatsuhi O. (2001) Stability robustness of 2-D systems described by the Fornasini-Marchesini model. IEEE Transactions on Circuits and Systems 12: 81–88
Zhu Q., Hu G.-D. (2011) Stability and absolute stability of a general 2-D nonlinear FM second model. IET Control Theory & Applications 5: 239–246
Zidong W., Xiaohui L. (2003) Robust stability of two-dimensional uncertain discrete systems. IEEE Signal Processing Letters 10: 133–136
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Kurek, J.E. Stability of nonlinear time-varying digital 2-D Fornasini-Marchesini system. Multidim Syst Sign Process 25, 235–244 (2014). https://doi.org/10.1007/s11045-012-0193-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11045-012-0193-4