A Model Matching Solution of Robust Observer Design for Time-Delay Systems

Uncertainties are unavoidable in practical situations and they have to be taken into consideration in control system design. In this paper, a method for designing a robust observer for linear time-delay systems is proposed. Under the assumption that the considered time-delay system is spectrally controllable and spectrally observable, a double Bézout factorization of its nominal transfer matrix is obtained. Next, based on this factorization, all stable observers for the nominal system are parameterized. By applying those observers on the real system, the parameterization transfer matrix has to be found such that the error between the real estimation and the nominal one is minimized. This problem is rewritten as an infinite dimensional model matching problem for different types of uncertainty. In order to solve this infinite dimensional model matching problem, it is transformed into a finite dimensional one, and therefore a suboptimal solution can be obtained using existing algorithms.