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

Volumn 36, Issue 6, 1989, Pages 830-837

  Agathoklis, Panajotis ^a   Jury, E I ^b   Mansour, Mohamed ^c  

^a UNIVERSITY OF VICTORIA   (Canada)

^b UNIVERSITY OF MIAMI   (United States)

^c ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84941499658     PISSN: 00984094     EISSN: None     Source Type: Journal    
DOI: 10.1109/31.90402     Document Type: Article

References (20)

1. M. S. Prekarski, “Algebraic characterization of matrices whose multivariable characteristic polynomial is Hurwitzian,” in Proc. Int. Symp. Operator Theory, Lubbock, TX, pp. 121-126, Aug. 1977.
2. J. H. Lodge and M. Fahny, “Stability and overflow oscillations in 2-D state-space digital filters,” IEEE Trans. Acoust. Speech, Signal Processing, vol. ASSP-29, pp. 1161-1171, 1981.
3. B. D. O. Anderson, P. Agathoklis, E. I. Jury, and M. Mansour, “Stability and the matrix Lyapunov equation for discrete 2-D systems,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 261-267, 1986.
4. E. Fornasini and G. Marchesini, “Stability analysis of 2-D systems,” IEEE Trans. Circuits Syst., vol. CAS-27, Dec. 1980.
5. Wu Sheng Lu, and E. B. Lee, “Stability analysis for two-dimensional systems via a Lyapunov approach,” IEEE Trans. Circuits Syst., vol. CAS-32, pp. 61-68, Jan. 1985.
6. M. Sendaula, “On the frequency dependent Lyapunov equation,” IEEE Trans. Circuits Syst., vol. CAS-33, pp. 428-430, Apr. 1986.
7. P. Agathoklis, E. I. Jury, and M. Mansour, “On the various forms and methods of solution of the Lyapunov equation for 2-D discrete systems,” in Proc. IEEE CDC, Fort Lauderdale, FL, pp. 1573-1578, Dec. 10-13, 1985.
8. B. D. O. Anderson and S. Vongpanitlerd, Network Analysis and Synthesis, A Modem Systems Theory Approach. Englewood Cliffs, NJ: Prentice-Hall, 1973.
9. P. P. Vaidyanathan, “The discrete-time bounded-real lemma in digital filtering,” IEEE Trans. Circuits Syst., vol. CAS-32, pp. 918-924, Sept. 1985.
10. D. C. Youla, “On the factorization of rational matrices,” IRE Trans. Inform. Theory, vol. IT-7, pp. 172-189, July 1961.
11. T. Kailath, Linear System. Englewood Cliffs, NJ: Prentice-Hall, 1980.
12. B. D. O. Anderson, “An algebraic solution to the spectral factorization problem,” IEEE Trans. Automat. Contr., vol. AC-12, pp. 410-414, 1967.
13. R. P. Roesser, “A discrete state-space model for linear image processing,” IEEE Trans. Automat. Contr., vol. AC-20, pp. 1-10, 1975.
14. W. F. Arnold and A. J. Laub, “Generalized eigenproblem algorithms and software for algebraic Riccati equations,” Proc. IEEE, vol. 27, pp. 1746-1754, Dec. 1984.
15. B. D. O. Anderson, K. L. Hitz, and N. D. Drew, “Recursive algorithm for spectral factorization,” IEEE Trans. Automat. Contr., vol. CAS-21, pp. 742-750, Nov. 1974.
16. F. R. Gantmacner, Theory of Matrices. New York: Chelsea, 1959.
17. K. S. Narenda and J. H. Taylor, Frequency Domain Criteria for Absolute Stability, New York: Academic, 1973.
18. R. Saeks, “The factorization problem-A survey,” Proc. IEEE, vol. 64, pp. 90-95, Jan. 1976.
19. P. Agathoklis, “Lower bounds for the stability margin of discrete 2-dimensional systems based on the 2-dimensional Lyapunov equation,” IEEE Trans. Circuits Syst., vol. CAS-35, pp. 745-749, June 1988.
20. P. Agathoklis, E. I. Jury, and M. Mansour, “The computation of positive definite solutions to the 2-D Lyapunov equation via a matrix Riccati equation,” in Proc. IEEE Int. Symp. on ISCAS 88, Helsinki, Finland, pp. 349-352, June 1988.