Geodesic
Stability of the solutions of the simplest space-distributed discrete equations
Modelirovanie i analiz informacionnyh sistem, Tome 24 (2017) no. 5, pp. 537-549.

Voir la notice de l'article provenant de la source Math-Net.Ru

The stability of the solutions of the linear equations arising in the theory of two-dimensional digital filtration is studied. The different statements of the initial value problem are analysed. As the basic results, the corresponding stability criterion is obtained for each of them.
Keywords: discrete equations, stability, boundary value problems, spectral set. 
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S. A. Kashchenko. Stability of the solutions of the simplest space-distributed discrete equations. Modelirovanie i analiz informacionnyh sistem, Tome 24 (2017) no. 5, pp. 537-549. http://geodesic.mathdoc.fr/item/MAIS_2017_24_5_a1/

[1] Chang T., “Limit cycles in a two-dimensional first-order digital filter”, IEEE Trans. Ckts. and Syst., 24 (1977), 15–19 | DOI | MR | Zbl

[2] El-Agizi N. G., Fahmy M. M., “Sufficient conditions for the nonexistence of limit cycles in two-dimensional digital filters”, IEEE Trans. Ckts. and Syst., 26 (1979), 402–406 | DOI | MR | Zbl

[3] Maria G. A., Fahmy M. M., “Limit cycle oscillations in first-order two-dimensional digital filters”, IEEE Trans. Ckts. and Syst., 22 (1975), 246–251 | DOI | MR

[4] Bose T., Brown D. P., “First-order 2-D periodically shift varying digital filters without limit cycles”, Proc. IEEE Southeastcon (1988), 619–623

[5] El-Agizi N. G., Fahmy M. M., “Two-dimensional digital filters with no overflow oscillations”, IEEE Trans. Acous., Speech and Signal Process., 27 (1979), 465–469 | DOI | MR | Zbl

[6] Lodge J. H., Fahmy M. M., “Stability and overflow oscillations in 2-D state-space digital filters”, IEEE Trans. Acous., Speech and Signal Process, 29 (1981), 1161–1171 | DOI | MR

[7] Bose T., Brown D. P., “Limit cycles in 2-D linearshift varying digital filters”, Proc. 31st Midwest Symp. on Ckts. and Syst. (1988)

[8] Bose T., Brown D. P., “Limit cycles in first-order two-dimensional digital filters”, Proc. IEEE Southeastcon (1989), 371–375