Brief Nonlinear observer design via passivation of error dynamics

Authors:
H. Shim;J. H. Seo;A. R. Teel
Affiliations:
Division of Electrical and Computer Engineering, Hanyang University, Seoul 133-791, South Korea;School of Electrical Engineering, Seoul National University, Seoul 151-742, South Korea;CCEC, Electrical and Computer Engineering Department, University of California, Santa Barbara, CA 93106-9560, USA
Venue:
Automatica (Journal of IFAC)
Year:
2003

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Abstract

We present a new design scheme of nonlinear state observers (global, full order, asymptotic observers) through passivation of the error dynamics. In order to consider passivity of the error dynamics for the observer problem, we place a conceptual input and output on the generalized error dynamics which also includes the plant, and the strictness of passivity is extended with respect to a set in which the estimation error becomes zero. Then, output feedback passivation for the error dynamics will lead to the construction of a state observer. It is also shown that a nonlinear observer is generally vulnerable to measurement disturbance, in the sense that even an arbitrarily small measurement disturbance can lead to a blowup of the error state. However, due to the passivity of the error dynamics, the proposed nonlinear injection gain can be easily modified for the observer to be robust to measurement disturbances.