Design And Simulation Of Robust Observer For Fractional Order Uncertain Singular Systems

Fractional-order systems (i.e. systems containing fractional derivatives and/or integrals) have been studied by many authors in engineering sciences from an application point of view. Many systems can be described with the help of fractional derivatives. These systems are recognized as display fractional-order dynamics:electromagnetic systems, dielectric polarization, viscoelastic systems chaotic synchronization and secure communications.State estimation and observer design have been widely used in control, signal processing, failure detection, fault diagnosis problems and chaotic synchronization and secure communications. But the observer design problem of singular systems is seldom studied. Fractional singular observer design problem has not been reported.Most physical systems always contain various nonlinear uncertainties, which are important to the stability analysis and observer design. So research on this kind of fractional-order system has a strong practical background. The present paper considers the stability problem and the design problem of robust observer for fractional-order uncertain singular systems. The main work of this paper is summarized as follows:Firstly, a brief overview of the fundamental theories of fractional calculus, state observer and research status of the application are given, show the great significance of designing state observer for fractional-order singular systems. At the same time, the fractional-order uncertain singular system is described.Secondly, a sufficient condition for the admissibility of observer-based fractional-order singular systems is presented. By using matrix singular value decomposition (SVD) and the LMI techniques, obtaining a sufficient condition for the controller design, and method of designing an observer for fractional-order singular systems based on LMI with the fractional commensurate order α (1≤α<2) are derived. A numerical example demonstrates the validity of this approach.Finally, a sufficient condition for the admissibility of observer-based fractional-order uncertain singular systems robust control is presented. A sufficient condition for the controller design is obtained. A method of designing robust observer for fractional-order uncertain singular systems based on LMI with the fractional commensurate order α (1≤α<2) is derived. Also a numerical example demonstrates the validity of this approach.