Stabilization of irrational transfer functions by controllers with internal loop

Transfer functions are called well-posed if they axe bounded and analytic on some right half-plane. Two concepts of L-2-stabilization are analyzed for well-posed transfer functions: the usual one, as in Figure 3, and a more general one called stabilization with internal loop, see Figure 4. In both cases we obtain a complete parametrization of all stabilizing controllers in terms of a doubly coprime factorization of the original transfer function. Moreover, the connection between the two stabilization concepts is clarified. We analyze two special subclasses of stabilizing controllers with internal loop, called canonical and dual canonical controllers. We show that, in a certain sense, every stabilizing controller with internal loop is equivalent to a canonical controller, and also to a dual canonical controller