Abstract
This paper studies the notion of output-input stability, which is a variant of the minimum-phase property for general smooth nonlinear control systems. In the spirit of the "input-to-state stability" philosophy, the definition of the new concept requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of output-input stable systems includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. A characterization of output-input stability for SISO systems is given in terms of suitable relative degree and detectability concepts.
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