Stability of discrete non-unit memory linear repetitive processes—a two-dimensional systems interpretation

International Journal of Control

Volumn 63, Issue 3, 1996, Pages 457-482

  Rocha, P ^a   Rogers, E ^b   Owens, D H ^c  

^a UNIVERSITY OF AVEIRO   (Portugal)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^c UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FEEDBACK CONTROL; LYAPUNOV METHODS; STABILITY; STATE SPACE METHODS; SYSTEM THEORY;

DISCRETE LINEAR REPETITIVE PROCESSES; ROESSER MODEL;

CONTROL SYSTEM ANALYSIS;

EID: 0030084674     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207179608921852     Document Type: Article

References (17)

1. Agathokus, P., 1988, Lower bounds for the stability margin of discrete two-dimensional systems based on the two-dimensional Lyapunov equation. IEEE Transactions on Circuits and Systems, 35, 745-749
2. Agathoklis, P., Jury, E. L, and Mansour, M., 1989, The discrete-time strictly bounded real lemma and the computation of positive definite solutions to the 2-D Lyapunov equation. IEEE Transactions on Circuits and Systems, 36, 830-837; 1990, An algebraic test for internal stability of 2-D discrete systems. Realisation and Modelling in System Theory, edited by M. A. Kaashoek, et ai (Boston, Mass: Birkhàuser).
3. Anderson, B. D. O, and Vongpanithlerd, S., 1973, Network Analysis and Synthesis-a Modern Systems Theory Approach (Englewood Cliffs, NJ: Prentice Hall).
4. Anderson, B. D. O., Agathokus, P., Jury, E. L, and Mansour, M., 1986, Stability and the matrix Lyapunov equation for discrete 2-dimensional systems. IEEE Transactions on Circuits and Systems, 33, 261-266.
5. Edwards, J. B., 1974, Stability problems in the control of multipass processes. Proceedings of the Institution of Electrical Engineers, 121, 1425-1431.
6. Fadalj, M. S., and Gnanasekaran, R., 1989, Normal matrices and their properties: application to 2-D system stabilisation. IEEE Transactions on Circuits and Systems, 36, 873-875.
7. Goodman, D., 1977, Some stability properties of two-dimensional linear shift invariant digital filters. IEEE Transactions on Circuits and Systems, 24, 201-208.
8. Huang, T. S., 1972, Stability of two-dimensional and recursive filters. IEEE Transactions on Audio and Electroacoustics, 20, 158-163.
9. Lancaster, P., and Tismenetsky, M., 1985, The Theory of Matrices (London, U.K.: Academic Press).
10. Lim, J. S., 1990, Two Dimensional Signal and Image Processing (Englewood Cliffs, NJ: Prentice Hall).
11. Lodge, J. H., and Fahmy, M., 1981, Stability and overflow oscillations in 2-D state space filters. IEEE Transactions on Acoustics, Speech and Signal Processing, 29, 1161-1171.
12. Lu, W. S., and Lee, E. B., 1985, Stability analysis for two-dimensional systems via a Lyapunov approach. IEEE Transactions on Circuits and Systems, 32, 61-68.
13. Piekarski, M. S., 1977, Algebraic characterisation of matrices whose multivariable characteristic polynomial is Hurwitzian. Proceedings of the International Symposium on Operator Theory, Lubbock, Texas, U.S.A., pp. 121-126.
14. Roesser, R. P., 1975, A discrete state space model for linear image processing. IEEE Transactions on Automatic Control, 20, 1-10.
15. Rogers, E., and Owens, D. H., 1990, 2D transfer functions and stability tests for discrete linear multipass processes. Realisation and Modelling in Systems Theory, edited by M. A. Kaashoek (Boston, Mass: Birkhàuser), pp. 351-356; 1992, Stability Analysis for Linear Repetitive Processes, Lecture Notes in Control and Information Sciences Series, Vol. 175 (Berlin: Springer-Verlag); 1995, Some simple structure stabilising control laws for linear repetitive processes. In preparation.
16. Shanks, J. L., Treitel, S., and Justice, J. H., 1972, Stability and synthesis of two dimensional recursive filters. IEEE Transactions on Audio and Electroacoustics, 20 (2).
17. Smyth, K. J., 1992, Computer aided analysis for linear repetitive processes. Ph.D. thesis, University of Strathclyde, Glasgow, U.K.