The extended Luenberger observer for nonlinear systems (Q579179)

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.