H∞ Synthesis of Nonlinear Feedback Systems in a Volterra Representation

[+] Author and Article Information
J. W. Glass, M. A. Franchek

Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-1077

J. Dyn. Sys., Meas., Control 124(3), 382-389 (Jul 23, 2002) (8 pages) doi:10.1115/1.1485749 History: Received September 01, 2000; Online July 23, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Lu,  Wei-Min, and Doyle,  John C., 1994, “H Control of Nonlinear Systems Via Output Feedback: Controller Parameterization,” IEEE Trans. Autom. Control, 39(12), pp. 2517–2521.
Ball,  Joseph A., Helton,  J. William, and Walker,  Michael L., 1993, “H Control for Nonlinear Systems With Output Feedback,” IEEE Trans. Autom. Control, 38(4), pp. 546–559.
Ball,  Joseph A., Kachroo,  Pushkin, and Kerner,  Arthur J., 1999, “H Tracking Control for a Class of Nonlinear Systems,” IEEE Trans. Autom. Control, 44(6), June, pp. 1202–1206.
Yung,  Chee-Fai, Wu,  Jenq-Lang, and Lee,  Tsu-Tian, 1998, “H Control for More General Nonlinear Systems,” IEEE Trans. Autom. Control, 43(12), Dec., pp. 1724–1727.
Isidori,  Alberto, and Kang,  Wei, 1995, “H Control Via Measurement Feedback for General Nonlinear Systems,” IEEE Trans. Autom. Control, 40(3), Mar., pp. 466–471.
Hardt,  Micheal, Helton,  J. William, and Kreutz-Delgado,  Kenneth, 2000, “Numerical Solution of Nonlinear H2 and H Control Problems With Application to Jet Engine Compressors,” IEEE Trans. Autom. Control, 8(1), Jan., pp. 98–111.
James,  M. R., and Yuliar,  S., 1995, “Numerical Approximation of the H Norm for Nonlinear Systems,” Automatica, 31(8), pp. 1075–1086.
Camilli,  Fabio, 1998, “Computation of the H Norm for Nonlinear Systems: A Convergence Result,” Syst. Control Lett., 28, pp. 139–150.
Tuan, H. D., Hosoe, S., Ono, E., and Apkarian, P., 1999, “Nonlinear H Control for an Integrated Suspension Via Parameterized Linear Matrix Inequality Characterizations,” Proceedings of the American Control Conference, June, pp. 3173–3176.
Corless, Martin, 1998, “Lyapunov Based Analysis and Control Design,” Proceedings of the ASME Dynamic Systems and Control Division, Nov., pp. 555–561.
Bendat, J. S., 1990, Nonlinear System Analysis and Identification From Random Data, Wiley, New York.
Shah,  M., and Franchek,  M. A., 1999, “Frequency Based Controller Design for a Class of Hammerstein Type Nonlinear Systems,” Int. J. Robust Nonlinear Control, 9(12), pp. 825–840.
Glass,  John W., and Franchek,  Matthew A., 2000, “Stability of Nonlinear Feedback Systems in a Volterra Representation,” Int. J. Robust Nonlinear Control, 10(10), Aug., pp. 799–819.
Schetzen, D. K., 1980, Volterra and Wiener Theory of Nonlinear Systems, Wiley, New York.
Franchek,  Matthew A., 1996, “Selecting the Performance Weightes for the μ and H Synthesis Methods for SISO Regulating Systems,” ASME J. Dyn. Syst., Meas., Control, 118, Mar., pp. 126–131.
Herman,  P., and Franchek,  M. A., 1998, “Direct Connection Between Time-Domain and Performance and Frequency-Domain Characteristics,” Journal of Robust and Nonlinear Control, 8(12), Oct., pp. 1021–1042.
Jayasuria,  S., and Song,  J. W., 1996, “On the Synthesis of Compensators for Nonovershooting Step Response,” ASME J. Dyn. Syst., Meas., Control, 118, pp. 757–763.
Doyle, J. C., Francis, B. A., and Tannenbaum, A. R., 1992, Feedback Control Theory, Macmillan, New York.
Green, Micheal, and Limebeer, David J. N., 1995, Linear Robust Control, Prentice Hall, Englewood Cliffs, NJ.


Grahic Jump Location
Trade-off between performance and stability
Grahic Jump Location
Engine speed response for a 15 Nm load
Grahic Jump Location
Actuator response for a 15 Nm load
Grahic Jump Location
Mapping C:U=Re through F(U) to a simple closed contour Γ for the design example



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In