The global existence of nonlinear observers with linear error dynamics: A topological point of view

In this paper we show that under suitable assumptions, there exists a global homeomorphism Ψ(=Φ-1)Ψ(=Φ-1) of RnRn which maps a nonlinear system x˙=f(x),x(0)=x0,y=h(x) onto a linear system with output injection z˙=Az+β(y),z(0)=Ψ(x0). Thus, an observer for state x   can be directly constructed as x^˙=f(x^)+β(y)-β(h(x^)), which is a generalized version of Luenberger observer. An important feature of the obtained result is that there is no need to find the corresponding change of coordinates ΨΨ explicitly, which is different from current various existing approaches.