Abstract
The Youla-Kucera parametrization, a method to parametrize all stabilizing controllers, is developed for linear and nonlinear systems based on their stable image and kernel representations. As a stepping stone of parametrizing nonlinear controllers for contraction, we investigate in this paper stable image and kernel representations for variational systems. In particular, we construct stable inner image (resp. co-inner kernel) representations having stable left (resp. right) inverses based on differential Riccati equations for contraction analysis.
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