Nonlinear observer design via passivation of error dynamics

• Published in: Automatica (Oxford) Vol. 39; no. 5; pp. 885 - 892
• Main Authors: Shim, H., Seo, J.H., Teel, A.R.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2003; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; Feedback passivation; Measurement noise; Nonlinear observers; Observer Lyapunov function; Nonlinear observers; Measurement noise; Observer Lyapunov function; Feedback passivation; Measurement; Input output; Estimation error; Error estimation; Feedback regulation; Numerical method; Non linear system; Passivity; Feedback; Dynamics; Interconnection; Integrated circuit; Observer; Lead; Asymptotic approximation; Measurement method; Non linear effect; Lyapunov function; Passivation
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/S0005-1098(03)00023-2

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.