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This paper is concerned with the state-space parametrization of all nonlinear stabilizing controllers via detectable kernel representations. We adopt ISS as the operator stability, and give the characterization of detectable kernel representations based on it. Then we will give a unified result of Youla parametrization for nonlinear systems which is valid both locally and globally in its state-space realization, while the existing result in conventional input/output approach is valid only in global setting, namely, it is only applicable when a global stabilizing controller and a global state observer are found.

Youla Parametrization for Nonlinear Systems Based on Input-to-State Stability