Characterization of all nonlinear stabilizing controllers via observer based kernel representations

This paper is concerned with the characterization of all nonlinear stabilizing controllers. Observer based kernel representations are introduced to avoid the difficulty which occurs in constructing the state-space realizations of input-output operators. By using observer based kernel representations, the parametrization of all the stabilizing plant-controller pairs is derived which is equivalent to the state-space parametrization. In addition the relationship between the kernel representation approach and the existing state-space approach is clarified.