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The extended Luenberger observer for nonlinear systems. (English) Zbl 0624.93012
A procedure for designing an observer for an observable nonlinear single- input single-output system \(\dot x=f(x,u)\), \(y=h(x,u)\) is given. First an input dependent state space transformation of the form \(x=w(x^*,u,\dot u,...,u^{(n-1)})\) which brings the nonlinear system into a nonlinear observer canonical form is determined. This in principle requires integration of nonlinear partial differential equations. Via an extended linearization procedure this is avoided. This method is what the author calls an extended Luenberger observer. The methods are illustrated by means of a second order polynomial system.
Reviewer: H.Nijmeijer

MSC:
93B07 Observability
93B10 Canonical structure
93C10 Nonlinear systems in control theory
93B55 Pole and zero placement problems
93B17 Transformations
93C15 Control/observation systems governed by ordinary differential equations
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