Positive and bounded real balancing for nonlinear systems - a controllability and observability function approach

In this paper we present a version of the balancing technique for nonlinear positive/bounded real systems. We discuss an approach to study related nonlinear systems that allow us to apply the theory of balancing based upon the Hankel operator and the corresponding singular value analysis. We provide balanced realizations of these systems. If we truncate them accordingly, the reduced order models will preserve their original structure, i.e., they are positive/bounded real.