5 Balanced Realization

Abstract

In this chapter, we introduce balancing for stable nonlinear descriptor systems. The approach used here is an extension of balancing for conventional systems. The classical ideas is extended naturally to the descriptor systems. That is, we will consider the past input and output energy of the descriptor systems. More precisely, the controllability function is defined as the past input energy and the observability function as the future output energy. Under certain sufficient conditions, these functions may be transformed into a form that gives us a measure of importance of a state component. A nonlinear descriptor system with its controllability and observability functions in this form is called a balanced representation.