Output–input stability implies feedback stabilization

Abstract

We study the recently introduced notion of output–input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. This paper develops the theory of output–input stability in the multi-input, multi-output setting. We show that output–input stability is a combination of two system properties, one related to detectability and the other to left-invertibility. For systems affine in controls, we derive a necessary and sufficient condition for output–input stability, which relies on a global version of the nonlinear structure algorithm. This condition leads naturally to a globally asymptotically stabilizing state feedback strategy for affine output–input stable systems.