Research On The Robustness Of The Fractional-Order System With Uncertain Parameters

This paper investigates the robust stability and feedback controller design problem of the fractional-order linear systems with nonlinear uncertain parameters. Recently, the fractional-order control systems have attracted increasing interest by more and more scholars.The robust stability analysis and robust controller design issues have been the main contents of the research in the control theory. Most physical systems always contain various nonlinear uncertainties, which are import for the robust stability analysis and controller design. So research on this kind of fractional-order system has a strong practical background.Fractional-order system with various nonlinear uncertainties studied in this paper includes system robust stability analysis and corresponding state-feedback controller design. Technique used is linear matrix inequality (LMI). Base on the characters'of different uncertainties, we derived different sufficient conditions of the asymptotically stability for the corresponding uncertainty system, and also give the method to design the state-feedback controller.Exactly, the main contents of the paper include:Firstly, the mathematical model problem of the fractional-order system with nonlinear uncertainty. Based on the practical physical system, the paper proposed two models, which are inherent connected with each other, to represent this kind of system. This mathematical model with the strong practical background will be mainly used in the paper.Secondly, supposing the uncertainty of the system is"Norm-bounded"uncertainty. We process the uncertain matrices of system carefully by zooming and other ways based on the feature of"Norm-bound"uncertainty. And then derive one sufficient condition of asymptotically stability for the system according to the stability criterion of the fractional-order system and LMI. Also the method used to design the state-feedback controller is given.Thirdly, assuming that the system uncertainty is"Polytope"uncertainty, we obtained one sufficient condition of asymptotically stability for this type system and also gave the method to design the state-feedback controller.Fourth, assuming that the system uncertainty satisfying"Matching condition". We treated the uncertain matrices equivalently, and obtained one sufficient and necessary condition of asymptotically stability for this type system and also gave the method to design the state-feedback controller.In the end, we do some numerical examples based on LMI toolbox of Matlab software to testify the effectiveness of our results.