The parallel projection operators of a nonlinear feedback system

Abstract
The authors define and study a pair of nonlinear parallel projection operators associated with a nonlinear feedback system. The input-output L/sub 2/-stability of a feedback system is shown to be equivalent to a coordinating of the input and output spaces, which is also equivalent to the existence of a pair of nonlinear parallel projection operators onto the graph of the plant and the inverse graph of the controller. These projections have equal norms whenever one of the feedback elements is linear. A bound on this norm is given in the case of passive systems with unity negative feedback.