Robust observer design for linear uncertain time-delay systems: A factorization approach

In this paper, a method to robust observers design for linear time-delay systems is developed. Firstly, all stable observers for a nominal model are parameterized based on a factorization of its transfer function. Applying those observers on the real system, the problem of selecting the parameterized term, such that the error between the real estimation and the nominal one is reduced, is transformed into an optimization problem (a model matching problem) for different uncertainty types. Finally, a suboptimal solution for this model matching problem is proposed in term of several finite dimensional H∞ optimization problem.