Global first harmonic bifurcation diagram for odd piecewise linear control systems

Dynamical Systems

Volumn 11, Issue 1, 1996, Pages 49-88

  Llibre, Jaume ^a   Ponce, Enrique ^b  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DESCRIBING FUNCTIONS; PIECEWISE LINEAR TECHNIQUES; SYSTEM STABILITY; TIME VARYING SYSTEMS;

GLOBAL FIRST HARMONIC BIFURCATION DIAGRAM; ODD PIECEWISE LINEAR CONTROL SYSTEMS;

LINEAR CONTROL SYSTEMS;

EID: 0030109902     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/02681119608806216     Document Type: Article

References (27)

1. Aizerman, M. A. (1963) Theory of Automatic Control (Pergamon, Oxford).
2. Allwright, D. J. (1977) Harmonic balance and the Hopf bifurcation theorem. Maths. Proceedings at the Cambridge Phil. Society 82, 453-467.
3. Alvarez, J., Suarez, R. and Alvarez, J. (1993) Planar linear systems with single saturated feedback. Systems and Control Letters 20, 319-326.
4. Arneodo, A., Coullet, P. and Tresser, C. (1981) Possible new strange attractors with spiral structure. Communications in Mathematical Physics 79, 573-579.
5. Atherton, D. P. (1982) Nonlinear Control Engineering (Describing Function Analysis and Design), 2nd edn (Van Nostrand Reinhold, New York).
6. Barnett, S. and Cameron, R. G. (1985) Introduction to Mathematical Control Theory, 2nd edn (Clarendon Press, Oxford).
7. Bogolyubov, N. N. and Krylov, N. M. (1934) Applications of New Nonlinear Mechanics Methods to the Investigation of Working of Synchronous Generators (OMTI, Moscow, in Russian).
8. Chen, C.-T. (1984) Linear System Theory and Design (Holt Rinehart and Winston).
9. Freire, R., Rodríguez-Luis, A. J., Gamero, E. and Ponce, E. (1993) A case study for homoclinic chaos in an autonomous electronic circuit. Physica D 62, 230-253.
10. Gantmakher, F. R. (1990) The Theory of Matrices, 2nd edn (Chelsea Publishing, New York).
11. Genesio, R. and Tesi, A. (1992) Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica 28, 531-548.
12. Gibson, J. E. (1963) Nonlinear Automatic Control (McGraw-Hill, New York).
13. Glover, J. N. (1989) Hopf bifurcations at infinity. Nonlinear Analysis 13, 1393-1398.
14. Goldfarb, L. C. (1947) On some nonlinear phenomena in regulatory system. Automatika i Telemekanika 349-383. Translation: Oldenburger, U. (ed.) (1956) Frequency Response. (Macmillan, New York).
15. Goldfarb, L. C. (1947) On some nonlinear phenomena in regulatory system. Automatika i Telemekanika 349-383. Translation: Oldenburger, U. (ed.) (1956) Frequency Response. (Macmillan, New York).
16. Huseyin, K. (1986) Multiple parameter stability theory and its applications. Oxford Engineering Series 18 (Clarendon Press, Oxford).
17. Khalil, H. K. (1992) Nonlinear Systems (Macmillan, New York).
18. Kochenburger, R. (1950) Frequency response method for analysis of a relay servomechanism. Transactions of the AIEE 69, 270-283.
19. Krenz, G. S. and Miller, R. K. (1986) Qualitative analysis of oscillations in nonlinear control systems: a describing function approach. IEEE Transactions on Circuits and Systems CAS-33, 562-566.
20. Llibre, J. and Sotomayor, J. (1996) Phase portraits of planar nonlinear control systems. Nonlinear Analysis, Theory, Methods and Applications (in press).
21. Mees, A. I. (1981) Dynamics of Feedback Systems (Wiley, New York).
22. Mees, A. I. and Chua, L. O. (1979) The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems. IEEE Transactions on Circuits and Systems CAS-26, 235-254.
23. Moila, J. L., Desages, A. and Romagnoli, J. (1991) Degenerate Hopf bifurcations via feedback system theory: higher-order harmonic balance. Chemical Engineering Science 46, 1475-1490.
24. Ogorzafek, M. J. (1986) Some observations on chaotic motion in single loop feedback systems. IEEE Proceedings of 25th Conference on Decision and Control, Athens, 588-589.
25. Sparrow, C. T. (1981) Chaos in a three-dimensional single loop feedback system with a piecewise linear feedback function. Journal of Mathematical Analytic Applications 83, 275-291.
26. Suarez, R., Alvarez, J. and Alvarez, J. (1992) Stability regions of closed loop linear systems with saturated linear feedback. Preprint.
27. Vidyasagar, M. (1993) Nonlinear Systems Analysis, 2nd edn (Prentice-Hall, Englewood Cliffs, NJ).