» Download Article

Authors
Murat Arcak; Michael Larsen; Petar Kokotovic

Digital Object Identifier (DOI)
10.3182/20020721-6-ES-1901.00264

Page Numbers:
262-262

Index Terms
nonlinear stabilization,absolute stability,Popov multiplier

Abstract
The goal of this paper is to transform classical absolute stability criteria into nonlinear design procedures which employ efficient numerical tools, such as LMI's. The paper starts with an analysis of an earlier circle criterion design, and shows that its feasibility is limited by conditions on the unstable part of the zero dynamics and on the relative degree. Then, an extended circle criterion design is developed which eliminates the relative degree obstacle. The restrictions on the zero dynamics are relaxed by using the Popov multiplier, which also reduces controller complexity. The results are illustrated on several physically motivated design examples.

References

[1] Arcak, M. and P. V. Kokotović (2001). Feasibility
    conditions for circle criterion designs. Systems
    and Control Letters 42(5), 405-412.
[2] Bernussou, J., J. C. Geromel and M. C. de Oliveira
    (1999). On strict positive real systems design:
    guaranteed cost and robustness issues. Systems
    and Control Letters 36, 135-141.
[3] Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan
     (1994). Linear Matrix Inequalities in System
     and Control Theory. Vol. 15 of SIAM Studies
     in Applied Mathematics. SIAM. Philadelphia,
     PA.
[4] Janković, M., M. Larsen and P.V. Kokotović
    (1999). Master-slave passivity design for stabilization
     of nonlinear systems. In: Proceedings
    of the 18th American Control Conference. San
    Diego, CA. pp. 769-773.
[5] Kokotović, P. V. and M. Arcak (2001). Constructive
     nonlinear control: a historical perspective.
    Automatica 37(5), 637-662.
[6] Krstić, M., I. Kanellakopoulos and P. Kokotović
    (1995). Nonlinear and Adaptive Control Design.
    John Wiley & Sons, Inc. New York.
[7] Popov, V. M. (1960). Criterion of quality for
    non-linear controlled systems. In: Preprints of
    the First IFAC World Congress. Butterworths.
    Moscow. pp. 173-176.
[8] Safonov, M. G., K. C. Goh and J. H. Ly (1994).
    Control system synthesis via bilinear matrix inequalities.
     In: Proceedings of the 1994 American
    Control Conference. Baltimore, MD. pp. 45-49.
[9] Tsiotras, P. and E. Velenis (2000). Low-bias control
     of AMB's subject to saturation constraints.
    In: Proceedings of the 2000 IEEE International
    Conference on Control Applications. Anchorage,
     Alaska.
[10] Zames, G. and P. L. Falb (1968). Stability conditions
      for systems with monotone and slope-restricted
      nonlinearities. SIAM Journal of Control
      and Optimization 6, 89-108.