Robust analysis and synthesis for a class of uncertain nonlinear systems with multiple equilibria

Systems and Control Letters

Volumn 53, Issue 2, 2004, Pages 89-105

  Yang, Ying ^a   Fu, Rao ^a   Huang, Lin ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Analysis and synthesis; LMI; Multiple equilibria; Nonlinear systems; Norm bounded parameter uncertainties

Indexed keywords

ASYMPTOTIC STABILITY; CLOSED LOOP CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; FEEDBACK CONTROL; LYAPUNOV METHODS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS);

ANALYSIS AND SYNTHESIS; MULTIPLE EQUILIBRIA; NORM-BOUNDED PARAMETER UNCERTAINITIES; ROBUST SYNTHESIS;

NONLINEAR SYSTEMS;

EID: 4344653760     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2004.02.024     Document Type: Article

References (21)

1. Abramovitch D.Y. Lyapunov redesign of analog phase-lock loops. IEEE Trans. Comm. 38(12):1990;2197-2202.
2. Corduneanu C. Integral Equations and Stability of Feedback Systems. 1973;Academic Press, New York.
3. P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI Control Toolbox User's Guide, 1st Edition, The MathWorks, 24 Prime Park Way, Natick, MA 01760-1500, 1995.
4. Gardner F.M. Phaselock Techniques. 1979;Wiley, New York.
5. Gelig A.K., Leonov G.A., Yakubovich V.A. The Stability of Nonlinear Systems with Nonunique Equilibrium. 1978;Nauka, Moscow. (in Russian).
6. ∞ control of systems under norm bounded uncertainties in all system matrices IEEE Trans. Automat. Control. 39(6):1994;1320-1322.
7. Haddad W.M., Kapila V. Fixed-architecture controller synthesis for systems with input-output time-varying nonlinearities. Int. J. Robust Nonlinear Control. 7(7):1997;675-710.
8. Leonov G.A., Burkin I.M., Shepeljavyi A.L. Frequency Methods in Oscillation Theory. 1992;Kluwer Academic Publishers, Dordrecht.
9. Leonov G.A., Noack A., Reitmann V. Asymptotic orbital stability conditions for flows by estimates of singular values of the linearization. Nonlinear Anal. 44(8):2001;1057-1085.
10. Leonov G.A., Ponomarenko D.V., Smirnova V.B. Frequency-Domain Methods for Nonlinear Analysis. 1996;World Scientific, Singapore.
11. Leonov G.A., Smirnova V.B. Stability and oscillations of solutions of integro-differential equations of pendulum-like systems. Math. Nachr. 177:1996;157-181.
12. Moser J. On nonoscillating networks. Quart. Appl. Math. 25:1967;1-9.
13. Narendra K.S., Taylor J.H. Frequency Domain Criteria for Absolute Stability. 1973;Academic Press, New York.
14. Popov V. Absolute stability of non-linear systems of automatic control. Automation Remote Control. 22:1961;857-875.
15. Rantzer A. On the Kalman-Yakubovich-Popov lemma. Systems Control Lett. 28(1):1996;7-10.
16. Rasvan V. Dynamical systems with several equilibria and natural Liapunov functions. Arch. Math. 34:1998;207-215.
17. Suykens J.A.K., Vandewalle J., Moor B.D. An absolute stability criterion for the Lur'e problem with sector and slope restricted nonlinearities. IEEE Trans. Circuits Systems I. 45(9):1998;1007-1009.
18. Vidyasagar M. Nonlinear System Analysis. 1993;Prentice-Hall, Englewood Cliffs, NJ.
19. N.E. Wu, Analog phaselock loop design using Popov criterion, in: Proceedings of the American Control Conference, 2002, pp. 16-18.
20. Xie L., Soh Y.C. Positive real control problem for uncertain linear time-invariant systems. Systems Control Lett. 24(4):1999;265-271.
21. ∞ controller synthesis for pendulum-like systems Systems Control Lett. 50(4):2003;263-276.