A STATE OBSERVER FOR SYSTEMS DESCRIBED BY FUNCTIONAL-DIFFERENTIAL EQUATIONS

The left characteristic matrix equation (LCME), introduced in earlier work, has proved to be a useful tool in the development of a feedback stabilization theory for delay systems. In this work, the dual notion of the right characteristic matrix equation (RCME) of a delay system is introduced via the state feedback stabilization of a dual system. As an application of the RCME, an observer theory is developed for distributed delay systems with distributed output delay using well-established finite dimensional system tools. It is shown that the separation property holds when the resulting observer is employed to generate the state feedback controls of the above-mentioned stabilization theory. Thus, by this work, the said state feedback stabilization theory is rendered input/output implementable. © 1990.