Generalizations of asymptotic gain characterizations of ISS to input-to-output stability

This paper generalizes to the case of output stability the study of a separation principle for input-to-state stability (ISS), which says that the ISS property can be expressed as the conjunction of stability and an asymptotic gain condition. It is shown that the direct generalization of ISS to outputs, known as input-to-output stability (IOS), only allows a separation principle under an additional condition of output Lagrange stability, meaning that outputs are stable with respect to initial outputs and inputs