Separation Principles for Input-Output and Integral-Input-to-State Stability

We present new characterizations of input-output-to-state stability. This is a notion of detectability formulated in the ISS framework. Equivalent properties are presented in terms of asymptotic estimates of the state trajectories based on the magnitudes of the external input and These results provide a set of separation principles for input-output-to-state stability – characterizations of the property as conjunctions of weaker stability notions. When applied to the notion of integral ISS, these characterizations yield analogous results.