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Robustness analysis of nonlinear
feedback systems: An input-output approach.

## T.T. Georgiou and M.C. Smith

## Abstract

This paper presents an approach to robustness analysis for nonlinear
feedback systems. We pursue a notion of model uncertainty based on
the closeness of input-output trajectories, and which is not tied to
a particular uncertainty representation, such as additive,
parametric, structured, etc. The basic viewpoint is to regard
systems as operators on signal spaces. We present two versions of a
global theory where stability is captured by induced norms or by
gain functions. We also develop local approaches (over bounded
signal sets), and give a treatment for systems with potential for
finite-time escape. We compute the relevant stability margin for
several examples and demonstrate robustness of stability for some
specific perturbations, e.g., small time delays. We also present
examples of nonlinear control systems which have zero robustness
margin and are destabilized by arbitrarily small gap perturbations.
The paper considers the case where uncertainty is present in the
controller as well as the plant, and the generalization of the
approach to the case where uncertainty occurs in several subsystems
in an arbitrary interconnection.