NORMALIZED COPRIME FACTORIZATIONS AND BALANCING FOR UNSTABLE NONLINEAR-SYSTEMS

In this paper we first study the normalized right and left coprime fac torizations of a nonlinear system from a state-space point of view. In order to do so, we introduce the notion of inner and co-inner nonline ar systems. Secondly we deal with balancing for unstable nonlinear sys tems. For linear systems there are several ways to approach this probl em, and we generalize the ideas of balancing the normalized coprime fa ctorization and of LQG balancing to the nonlinear case. LQG balancing can be seen as measuring the influence of a state component on a certa in future and past energy function. We extend this interpretation to t he nonlinear case. Furthermore we use the normalized coprime factoriza tion to give another way of balancing the unstable nonlinear system. W e give the relation between these two methods of balancing, which is s imilar to the relation in the linear case.