Stabilizing submanifolds with passive input-output relations

We study submanifold stabilization problems from an input-output perspective. For doing so, we consider feedback interconnections of relations of signals whose squared distance to a given submanifold has finite integral. In our framework, output feedback passivity of the feedforward relation and input strict passivity of the feedback relation with sufficiently large excess of passivity, both with respect to the integral squared distance of their signals to the submanifold under consideration, is sufficient for submanifold stabilization. We show that the distance of the signals in the feedback interconnection to the submanifold remains bounded for bounded exogenous inputs, thus extending the feedback theorem for passive systems to submanifold stabilization problems.