Diagnosis of time-delay fractional systems

In this paper, a model-based diagnosis method, called Luenberger diagnosis observer, recently developed for fractional order systems, is extended for time-delay fractional systems. A sufficient convergence condition of the fault indicator using Bilinear Matrix Inequalities is detailed. A numerical example illustrating the method's validity in detecting faults is finally presented.

I. Introduction

Diagnosis has always been a focus of interest to many researchers because it ensures the reliability of dynamical systems. There exist two main diagnosis methods; expert diagnosis and model-based diagnosis. The first approach does not require the system's model and it depends on the experience. The second one is more efficient. It refers to the system's model in detecting faults. Parameter estimation [10], parity-space [9] and observers [11], [19] are the most known model-based methods. Studies have shown that time-delays exist in many fields such as biological processes and hydraulic networks. They are defined by differential difference equations [1]. On the other hand, several dynamical processes can be characterized by fractional models. Fractional differentiation models are investigated through several applications such as control [17], identification [2], [5] and diagnosis [3], [4].