Controller parameterization for SISO and MIMO plants with time delay

Controller parameterization is a very fundamental problem in control theory. It provides an elegant and efficient way towards solving the stabilizing and design problem, with which all stabilizing controllers are characterized and thus a constrained design procedure can be replaced by an unconstrained optimization. In this paper we deal with the problem of characterizing all stabilizing controllers for single-input/singleoutput (SISO) plants with time delay and multi-input/multi-output (MIMO) plants with multiple time delays. A new parameterization is derived on the basis of the definition of the internal stability. The new parameterization does not depend on the coprime factorization of the plant and has similar form to that of the Youla parameterization for stable plants. An important merit of the proposed parameterization is that it reflects the internal model control (IMC) structure and thus has a very simple relationship to the sensitivity function and complementary sensitivity function. Numerical examples are given to illustrate the proposed parameterization. © 2006 Elsevier B.V. All rights reserved.