Research Papers

On Simple Design of Nonlinear Observers for Robust Stabilization of Nonlinear Systems

[+] Author and Article Information
Jacob Hammer

Department of Electrical
and Computer Engineering,
University of Florida,
Gainesville, FL 32611

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 19, 2014; final manuscript received February 18, 2015; published online March 26, 2015. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 137(7), 071011 (Jul 01, 2015) (10 pages) Paper No: DS-14-1342; doi: 10.1115/1.4029886 History: Received August 19, 2014; Revised February 18, 2015; Online March 26, 2015

Robust internal stabilization is a strong notion of stabilization, whereby stability is maintained regardless of small disturbances, noises, and uncertainties. In this paper, simple tools are developed for achieving robust internal stabilization of a rather large family of nonlinear systems. The main notion is that of a strict observer function, a function characterized by the following feature: subtracting a strict observer function from the differential equation of the controlled system results in an asymptotically stable differential equation. Strict observer functions are relatively easy to derive, and they directly yield robust asymptotic observers; the latter can be combined with robust state feedback controllers to achieve robust internal stabilization.

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Fig. 1

The observer–controller configuration

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Fig. 2

Static state feedback

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Fig. 3

An asymptotic observer O for the observed system Σ

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Fig. 4

The observer–controller configuration

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Fig. 5

Observer with disturbances

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Fig. 6

Internal stability of the observer–controller configuration

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Fig. 7

Robust state feedback




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