Nonlinear extension of Bode's integral based on an information-theoretic interpretation

Systems and Control Letters

Volumn 50, Issue 1, 2003, Pages 11-19

  Zang, Guoqiang ^a   Iglesias, Pablo A ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Bode's integral; Entropy; Inner outer factorizations; Sensitivity

Indexed keywords

ENTROPY; INTEGRATION; LINEAR SYSTEMS;

BODE INTEGRAL;

NONLINEAR SYSTEMS;

EID: 0042122606     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(03)00119-1     Document Type: Article

References (26)

1. Ball J.A., Helton J.W. Inner-outer factorization of nonlinear operators. J. Funct. Anal. 104:1992;363-413.
2. Ball J.A., van der Schaft A.J. J-inner-outer factorization, J-spectral factorization, and robust control for nonlinear systems IEEE Trans. Automat. Control. 41:1996;379-392.
3. Bode H.W. Network Analysis and Feedback Amplifier Design. 1945;Van Nostrand, Princeton, NJ.
4. Boyd S., Chua L.O. Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Trans. Circuits Systems. 32:1985;1150-1161.
5. Byrnes C.I., Lin W. Losslessness, feedback equivalence, and the global stabilization of discrete-time nonlinear systems. IEEE Trans. Automat. Control. 39:1994;83-98.
6. Cover T.M., Gacs P., Gray R.M. Kolmogorov's contributions to information theory and algorithmic complexity. Ann. Probab. 17:1989;840-855.
7. Doyle J.C., Francis B.A., Tannenbaum A.R. Feedback Control Theory. 1992;Macmillan, New York.
8. Freudenberg J.S., Looze D.P. Frequency Domain Properties of Scalar and Multivariable Feedback Systems. 1988;Springer, Berlin.
9. K. Glover, Minimum entropy and risk-sensitive control: the continuous time case, in: Conference on Decision Control, 1989, pp. 388-391.
10. ∞ norm bound and relations to risk sensitivity Systems Control Lett. 11:1988;167-172.
11. Iglesias P.A. An entropy formula for time-varying discrete-time control systems. SIAM J. Control Optim. 34:1996;1691-1706.
12. P.A. Iglesias, An analogue of Bode's integral for stable nonlinear systems: relations to entropy, in: Conference on Decision Control, 2001, pp. 3419-3420.
13. Iglesias P.A. A time-varying analogue of Jensen's formula. Integral Equations Operator Theory. 40:2001;34-51.
14. Iglesias P.A. Tradeoffs in linear time-varying systems. an analogue of Bode's sensitivity integral Automatica. 37:2001;1541-1550.
15. Iglesias P.A. Logarithmic integrals and system dynamics. an analogue of Bode's sensitivity integral for continuous-time, time-varying systems Linear Algebra Appl. 343-344:2002;451-471.
16. Iglesias P.A., Zang G. Szego's first limit theorem in terms of a realization of a continuous-time, time-varying system. Internat. J. Appl. Math. Comput. Sci. 11:2001;1261-1276.
17. Khalil H.K. Nonlinear Systems. 2nd Edition:1996;Prentice-Hall, Upper Saddle River, NJ.
18. Khargonekar P.P., Sontag E.D. On the relation between stable matrix fraction factorizations and regulable realizations of linear systems over rings. IEEE Trans. Automat. Control. 27:1982;627-638.
19. Kolmogorov A.N. On the Shannon theory of information in the case of continuous signals. IRE Trans. Inform. Theory. 2:1956;102-108.
20. Papoulis A. Probability, Random Variables, and Stochastic Processes. 2nd Edition:1984;McGraw-Hill, New York.
21. Peters M.A., Iglesias P.A. Continuous-time time-varying entropy. Math. Control Signals Systems. 10:1997;76-96.
22. Serón M.M., Braslavsky J.H., Goodwin G.C. Fundamental Limitations in Filtering and Control. 1997;Springer, London.
23. Serón M.M., Braslavsky J.H., Kokotović P.V., Mayne D.Q. Feedback limitations in nonlinear systems. from Bode integrals to cheap control IEEE Trans. Automat. Control. 44:1999;829-833.
24. 2-gain and Passivity Techniques in Nonlinear Control:2000;Springer, London.
25. G. Zang, P.A. Iglesias, Fading memory and stability, J. Franklin Inst., to appear.
26. Zhou K., Doyle J.C., Glover K. Robust and Optimal Control. 1996;Prentice-Hall, Upper Saddle River, NJ.