Sensitivity and robust stability of nonlinear input-output systems consisting of finitely many blocks

We construct a general model of a nonlinear input-output system consisting of finitely many blocks whose variables are in extended spaces. This model encompasses all configurations used in control which have several feedback and feedforward loops. We show that such a system is essentially the traditional MI-MO feedback system. Moreover, assuming that one block of the system is a plant affected by perturbations, we derive conditions guaranteeing linear insensitivity and/or robust stability of the whole system. In particular, we consider systems whose variables are continuous, vector-valued functions on [0, infinity), and whose blocks are described by nonlinear Volterra operators. The applications of the results are illustrated by several examples of feedback-feedforward systems.