Research On The Stability Of Fractional Linear Systems

Fractional order linear systems represent a wider class of complex dynamical systems,have received great attention recently,both from an academia and industry viewpoint.On the one hand,fractional order systems are more flexible,which makes the modeling of complex systems more accurate and achieves more challenging control requirements.On the other hand,compared with the traditional integer order controllers,fractional order controllers have better robustness and design freedom.With the unremitting efforts of researchers,fractional order systems have achieved many valuable results in numerical calculation,systems modeling,stability analysis and comprehensive control.Based on the research results,this thesis utilizes the algorithm and various inequality techniques to further investigate the stabilization of fractional order systems.The main contents of this thesis are presented as follows:1.In this thesis,the stabilization problem for rectangular descriptor fractional order systems with? ?(0,1]is studied.We design a fractional order dynamic compensator to make the closed-loop system a square descriptor fractional order system,and study two types of input signals of the compensator,which are state input signal case and output input signal case.Then we propose a necessary and sufficient condition to solve the state input signal case for the first time,and provide a sufficient condition for the output input signal case.2.The stabilization via static output feedback control for fractional order systems with input delay with? ?(0,1)is studied.Firstly,the system is transformed into an input-delayfree system by using Smith predictor.Then a new output feedback controller design is presented,and linear matrix inequalities(LMIs)based controller implementation algorithm is provided.It is worth noting that in this thesis,we apply the approximation algorithm,which extends from integer case to fractional case to implement the Smith predictor for the first time,and we also give the range of the parameters to reach the limit of the given approximation error.3.For the rectangular generalized fractional-order system and the fractional-order system with input delay,the static output feedback control problem is proposed.According to the characteristics of the system,different controller design methods are constructed,and the algorithm implemented by the controller is given using inequality and iteration techniques.The proposed methods reduce the conservativeness of existing results and are more widely used.Numerical examples verify the correctness and feasibility of the obtained results.