Discrete Time Positive-Real Lemma Revisited: The Discrete Time Counterpart of the Kalman-Yakubovitch Lemma

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 41, Issue 11, 1994, Pages 747-750

  Premaratne, Kamal ^a   Jury, Eliahu I ^a  

^a UNIVERSITY OF MIAMI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; LINEAR NETWORK SYNTHESIS; MATRIX ALGEBRA; SYSTEM STABILITY; TRANSFER FUNCTIONS;

DISCRETE-TIME POSITIVE REAL LEMMA; JURY LEE CRITERION; KALMAN YAKUBOVITCH LEMMA;

LINEAR NETWORKS;

EID: 0028547466     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.331529     Document Type: Article

References (17)

1. V. A. Yakubovitch, “The solution of certain matrix inequalities in automatic control theory,” Doklady Akademii Nauk SSSR, vol. 143, pp. 1304–1307, 1962.
2. R. E. Kalman, “Lyapunov functions for the problem of Lur'e in automatic control,” in Proc. Nat. Acad. Sci., vol. 49, pp. 201–205, 1963.
3. L. Hitz and B.D.O. Anderson, “Discrete positive-real functions and then-application to system stability,” in Proc. IEE, vol. 116, pp. 153–155, Jan. 1969.
4. B.D.O. Anderson, K. L. Hitz, and N. D. Diem, “Recursive algorithm for spectral factorization,” IEEE Trans. Circuits and Syst., vol. CAS-21, pp. 742–750, Nov. 1974.
5. E. I. Jury and B. W. Lee, “On the stability of a certain class of nonlinear sampled-data systems,” IEEE Trans. Automat. Cont., vol. AC-9, pp. 51–61, Jan. 1964.
6. E. I. Jury and M. Mansour, “On the terminology relationship between continuous and discrete system criteria,” Proc. IEEE, vol. 73, p. 844, Apr. 1985.
7. M.K.P. Mishra and A. K. Mahalanabis, “On the stability of discrete nonlinear feedback systems with state-dependant noise,” Intl. J. Syst. Sci., vol. 6, pp. 479–490, 1975.
8. N. O'Reilly and P. C. Byrne, “Frequency-domain condition for the existence of a Lyapunov functional for the problem of Lur'e,” IEEE Trans. Auto. Control, vol. AC-25, pp. 555–557, June 1980.
9. V. Singh, “Extended MKY lemma—What shall it be?” IEEE Trans. Automat. Cont., vol. AC-28, 627–628, May 1983.
10. S. Kodama, “Stability of nonlinear sampled-data systems,” IRE Trans. Automat. Cont., vol. AC-7, pp. 15–23, Jan. 1962.
11. J. B. Pearson and J. E. Gibson, “On the asymptotic stability of a class of saturating sampled-data systems,” IEEE Trans. Appl. Industry, vol. 81–86, Mar. 1964.
12. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
13. Y. Z. Tsypkin, “The absolute stability of large-scale, nonlinear, sampled-data systems,” Doklady Akademii Nauk SSSR, vol. 145, pp. 52–55, July 1962.
14. G. P. Szego, “On the absolute stability of sampled-data control systems,” in Proc. Nat. Acad. Sci., vol. 50, pp. 558–560, 1963.
15. E. I. Jury and B. W. Lee, “The absolute stability of systems with many nonlinearities,” Avtomatika i Telemekhanika, vol. 16, pp. 945–965, Jun. 1965.
16. V. Singh, “Lyapunov-based proof of Jury-Lee's criterion: Some appraisals,” IEEE Trans. Circuits and Syst., vol. CAS-32, pp. 396–398, Apr. 1985.
17. T. N. Sharma and V. Singh, “On the absolute stability of multivariable Discrete Time nonlinear systems,” IEEE Trans. Automat. Cont., vol. AC-26, pp. 585–586, Apr. 1981.