Abstract
This paper is focused on analyzing the practical bounded input bounded output (BIBO) stability concept originally introduced by Agathoklis and Bruton with respect to its applicability in n-D signal processing applications. By comparing the frequency response expected on basis of the transfer function to the Fourier transform of the actually measured impulse response of exemplary systems it is shown that the concept of practical stability cannot be a general n-D stability criterion for systems, in particular for signal processing applications, if roots of the given transfer function are not guaranteed to be close to the respective n-D BIBO stability region.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agathoklis P., Bruton L. T. (1983) Practical-BIBO stability of n-dimensional discrete systems. IEE Proceedings. Part G. Electronic Circuits & Systems 130(6): 236–242
Ben Mabrouk, W., Messaoud, H., & Garcia, G. (2009). Practical stability and stabilization of linear systems. In 17th Mediterranean conference on control and automation, MED ’09 (pp. 347–352). doi:10.1109/med.2009.5164565.
Bose N. K. (1982) Applied multidimensional systems theory. Van Nostrad-Reinhold, New York, NY
Galkowski K., Rogers E., Kummert A. (2009) Strong practical stability and stabilization of discrete linear repetitive processes. Multidimensional Systems and Signal Processing 20: 311–331
Goodman D. (1977) Some stability properties of two-dimensional linear shift-invariant digital filters. IEEE Transactions on Circuits and Systems 24(4): 201–208
Huang T. S. (1972) Stability of two-dimensional recursive filters. IEEE Transactions on Audio and Electroacoustics 20: 158–163
Jury E. I. (1978) Stability of multidimensional scalar and matrix polynomials. Proceedings of the IEEE 66(9): 1018–1047
Schauland, S., Velten, J., Kummert, A., & Galkowski, K. (2009). On the usability of practical stable n-D systems for signal processing applications. In IEEE international symposium on circuits and systems, 2009. ISCAS 2009 (pp. 317–320). doi:10.1109/iscas.2009.5117749.
Swamy M. N. S., Roytman L. M., Plotkin E. I. (1985) On stability properties of three- and higher dimensional linear shift-invariant digital filters. IEEE Transactions Circuits and Systems 32(9): 888–892
Velten J., Schauland S., Kummert A. (2012) Realization of multidimensional signal processing systems given in natural k-D state space description. Multidimensional Systems and Signal Processing 23(1–2): 281–290
Xu L., Saito O., Abe K. (1994) The design of practically-stable nD feedback systems. Automatica 30(9): 1389–1397
Xu L., Saito O., Abe K. (1996a) Practical internal stability of nD discrete systems. IEEE Transactions on Automatic Control 41(5): 756–761
Xu L., Saito O., Abe K. (1996b) Design of practically stable nD feedback systems: A state-space approach. International Journal of Control 64(1): 29–39
Xu L., Saito O., Abe K. (1997) nD control systems in a practical sense. Applied Mathematics and Computer Science (Special Issue on Recent Developments in Two-Dimensional Linear System Theory) 7(4): 907–941
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Schauland, S., Velten, J., Kummert, A. et al. Insufficiencies of practical BIBO stable n-D systems. Multidim Syst Sign Process 25, 3–15 (2014). https://doi.org/10.1007/s11045-012-0180-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11045-012-0180-9