Non-linear observer design by approximate error linearization

Abstract For a given non-linear system, an observer that provides exactly linear error dynamics can be computed by solving the so-called generalized characteristic equation (GCE). Unfortunately, the existence of a solution to the GCE is not a generic property. For unforced, scalar-output systems, we show how spline functions may be used to construct approximate solutions that minimize a norm of the non-linear terms obstructing linearization of the error dynamics. The resulting error dynamics are shown to be locally exponentially stable. A numerical example illustrates the design and performance of the observer.

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