Nonlinear observers: a circle criterion design and robustness analysis

Authors:
Murat Arcak;Petar Kokotović
Affiliations:
Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180-3590, USA;Department of Electrical, and Computer Engineering, University of California, Santa Barbara, CA 93106-9560, USA
Venue:
Automatica (Journal of IFAC)
Year:
2001

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Abstract

Globally convergent observers are designed for a class of systems with monotonic nonlinearities. The approach is to represent the observer error system as the feedback interconnection of a linear system and a time-varying multivariable sector nonlinearity. Using LMI software, observer gain matrices are computed to satisfy the circle criterion and, hence, to drive the observer error to zero. In output-feedback design, the observer is combined with control laws that ensure input-to-state stability with respect to the observer error. Robustness to unmodeled dynamics is achieved with a small-gain assignment design, as illustrated on a jet engine compressor example.