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) of Rn 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 Ψ explicitly, which is different from current various existing approaches.