Concepts of strict positive realness and the absolute stability problem of continuous-time systems

Automatica

Volumn 34, Issue 9, 1998, Pages 1071-1082

  Xiao, Chengshan ^a   Hill, David J ^b  

^a NORTEL NETWORKS   (Canada)

^b NONE

Author keywords

Absolute stability; Continuous time systems; Nonlinear control; Nonlinear feedback systems; Wide strict positive realness

Indexed keywords

FEEDBACK; FREQUENCY DOMAIN ANALYSIS; POLES AND ZEROS; SYSTEM STABILITY;

CONTINUOUS-TIME SYSTEMS; WIDE POSITIVE REALNESS (WPR); WIDE STRICT POSITIVE REALNESS (WSPR);

NONLINEAR CONTROL SYSTEMS;

EID: 0032163025     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(98)00049-1     Document Type: Article

References (47)

1. Anderson, B. D. O. (1966). Stability of control systems with multiple nonlinearities. J. Franklin Inst., 282, 155-160.
2. Anderson, B. D. O. (1967). A system theory criterion for positive real matrices. SIAM J. Control, 5, 171-182.
3. Anderson, B. D. O. and S. Vongpanitlerd (1973). Network Analysis and Synthesis. Prentice-Hall, Englewood Cliffs, NJ.
4. Aizerman, M. A. and F. R. Gantmacher (1964). The Absolute Stability of Regulator Systems. Holden Day, San Franciso.
5. Brockett, R. W. and J. L. Willems (1965). Frequency domain stability criteria, Parts I and II. IEEE Trans. Automat. Control, AC-10, 255-261, 407-413.
6. Desoer, C. A. (1965). A generalization of the Popov criterion. IEEE Trans. Automat. Control, AC-10, 182-185.
7. Dewey, A. G. (1966). On the stability of feedback systems with one differentiable nonlinear element. IEEE Trans. Automat. Control, AC-11, 485-491.
8. Dewey, A. G. and E. I. Jury (1966). A stability inequality for a class of nonlinear feedback systems. IEEE Trans. Automat. Control, AC-11, 54-62.
9. Haddad, W. M. and V. Kapila (1995). Absolute stability criteria for multiple slope-restricted monotonic nonlinearities. IEEE Trans. Automat. Control, 40, 361-365.
10. Halanay, A. and V. Rasvan (1991). Absolute stability of feedback systems with several differentiable non-linearities. Int. J. Systems Sci., 22, 1911-1927.
11. Ibrahim, E. S. and Z. V. Rekasius (1964). A stability criterion for nonlinear feedback systems. IEEE Trans. Automat. Control, AC-9, 154-159.
12. Ioannou, P. and G. Tao (1987). Frequency domain conditions for strictly positive real functions. IEEE Trans. Automat. Control, 32, 53-54.
13. Josselson, R. and G. V. S. Raju (1974). Absolute stability of control systems with many sector and slope-restricted non-linearities. Int. J. Control, 19, 609-614.
14. Jury, E. I. and B. W. Lee (1965). The absolute stability of systems with many nonlinearities. Automat. Remote Control, 16, 943-961.
15. Kalman, R. E. (1963). Lyapunov functions for the problem of Lur'e in automatic control. Proc. Nat. Acad. Sci., 49, 201-205.
16. Khalil, H. K. (1992). Nonlinear Systems Macmillan, New York.
17. Landau, I. D. (1979). Adaptive Control - The Model Reference Approach. Marcel Dekker, New York.
18. Lefschetz, S. (1965). Stability of Nonlinear Control Systems. Academic Press, New York.
19. Lozano-Leal, R. and S. M. Joshi (1990). Strictly positive real transfer functions revisited. IEEE Trans. Automat. Control, 35, 1243-1245.
20. Lozano-Leal, R. and S. M. Joshi (1995). Reply to "Comments on 'Strictly positive real transfer functions revisited'". IEEE Trans. Automat. Control 40, 1799-1800.
21. Lur'e, A. I. and V. N. Postnikov (1944). On the theory of stability of control systems. Prikl. Mat. Meh., 8(3).
22. Marquez, H. J. and C. J. Damaren (1995). Comments on 'Strictly positive real transfer functions revisited'. IEEE Trans. Automat. Control, 40, 478-479.
23. Moore, J. B. and B. D. O. Anderson (1968). A generalization of the Popov criterion. J. Franklin Inst., 285, 488-492.
24. Narendra, K. S. and R. M. Goldwyn (1964). Existence for quadratic type Liapunov functions for a class of nonlinear systems. Int. J. Engng Sci., 2, 367-377.
25. Narendra, K. S. and C. P. Neuman (1967). Stability of continuous time dynamical systems with m-feedback nonlinearities. AIAA J., 5, 2021-2027.
26. Narendra, K. S. and J. H. Taylor (1973). Frequency Domain Criteria for Absolute Stability. Academic Press, New York.
27. O'Reilly, N. and P. C. Byrne (1980). Frequency-domain condition for the existence of a Lyapunov functional for the problem of Lurie. IEEE Trans. Automat. Control, AC-25, 555-557.
28. O'Reilly, N. and P. C. Byrne (1982). Author's reply to 'A note on the extended MKY lemma'. IEEE Trans. Automat. Control, AC-27, 1264.
29. Popov, V. M. (1961). Absolute stability of nonlinear systems of automatic control. Automat. Remote Control, 22, 857-875.
30. Popov, V. M. (1973). Hyper stability of Control Systems. Springer, Berlin.
31. Purkayastha, S. and A. K. Mahalanabis (1971). An extended MKY lemma and its application. IEEE Trans. Automat. Control, AC-16, 366-367.
32. Sharma, T. N. and V. Singh (1980). On the absolute stability of continuous-time nonlinear systems. IEEE Trans. Automat. Control, AC-25, 332-334.
33. Singh, V. (1982). A note on the extended MKY lemma. IEEE Trans. Automat. Control, AC-27, 1264.
34. Singh, V. (1983). Extended MKY lemma - what shall it be? IEEE Trans. Automat. Control, AC-28, 627-628.
35. Singh, V. (1984). A stability inequality for nonlinear feedback systems with slope-restricted nonlinearity. IEEE Trans. Automat. Control, AC-29, 743-744.
36. Srinath, M. D., M. A. L. Thathacher and H. K. Ramapriyan (1968). Absolute stability of systems with multiple non-linearities. Int. J. Control, 7, 365-375.
37. Tao, G. and P. A. Ioannou (1988). Strictly positive real matrices and the Lefschetz-Kalman-Yakubovich lemma. IEEE Trans. Automat. Control, 33, 1183-1185.
38. Thathacher, M. A. L. and M. D. Srinath (1970). An improved stability criterion for a system with a non-monotone non-linearity. Int. J. Control, 12, 145-155.
39. Vidyasagar, M. (1993). Nonlinear Systems Analysis, 2nd edn. Englewood Cliffs, Prentice Hall, NJ.
40. Wen, J. T. (1988). Time domain and frequency domain conditions for strict positive realness. IEEE Trans. Automat. Control, 33, 988-992.
41. Willems, J. L. (1967a). Comments on 'A stability inequality for a class of nonlinear feedback systems'. IEEE Trans. Automat. Control, AC-12, 223-224.
42. Willems, J. L. (1967b). An extension of'Comments on a stability inequality for a class of nonlinear feedback systems'. IEEE Trans. Automat. Control, AC-12, 339-340.
43. Yakubovich, V. A. (1962). The solution of certain matrix inequalities in automatic control. Dokl. Akad. Nauk. SSSR, 143, 1304-1307.
44. Yakubovich, V. A. (1965a). Frequency conditions for the absolute stability and dissipativity of control systems with a single differentiable nonlinearity. Sov. Math., 6, 98-101.
45. Yakubovich, V. A. (1965b). The matrix-inequality method in the theory of the stability of nonlinear control systems, II. absolute stability in a class of nonlinearities. Automat. Remote Control, 16, 577-592.
46. Youla, D. C. (1961). On the factorization of rational matrices. IEEE Trans. Inform. Theory, IT-7, 172-189.
47. Zames, G. (1966). On the input-output stability of time-varying nonlinear feedback systems, Parts I and II. IEEE Trans. Automat. Control, AC-11, 228-238, 465-476.