The extended Luenberger observer for nonlinear systems. (English) Zbl 0624.93012

Zeitz, M.

Syst. Control Lett. 9, 149-156 (1987).

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

Keywords:

observer; nonlinear single-input single-output system; state space transformation; nonlinear observer canonical form; extended Luenberger observer

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