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 ker-nel representations are introduced to avoid the diculty which occurs in constructing the state-space realizations of input-output operators. By using observer based ker-nel representations, the parametrization of all the stabi-lizing plant-controller pairs is derived which is equivalent to the state-space parametrization. In addition the rela-tionship between the kernel representation approach and the existing state-space approach is claried.