Research On Stability Analysis And Controller Design For Several Kinds Of Nonlinear Fractional-order System

In recent years,the research of fractional calculus has been paid more and more attention in the field of control system.The nonlinear system is more straightforward to describe the real physical system than the linear system.Naturally,many results of the linear system are extended to the nonlinear system,so the nonlinear system has been extensively studied in recent years.In the course of study,many scholars have done a lot of valuable work about nonlinear system problems and applied them to control various dynamic processes,including integer order systems and fractional order systems,thus these work improves the stability and control performance of the system.Aiming at the stability problem of nonlinear fractional order system,the main work can be summarized into the following aspects:1)The output feedback control problem for a class of nonlinear fractional order uncertain systems was studied.Firstly,based on the Lyapunov stability theorem,the nonlinear fractional order system was stabilized by output feedback control.Secondly,the sufficient conditions of stability in term of linear matrix inequality(LMI)were obtained by matrix singular value decomposition(SVD).Finally,the correctness and validity of the conclusion were verified by simulating the fractional Lü system.2)The feedback control problem for a class of fractional triangular systems was researched.Firstly,based on Lyapunov stability theorem,the stability condition of nonlinear fractional order system and the design of feedback controller were presented by back-stepping method.Secondly,by variable conversion,the problem of control and synchronization for the master and slave fractional R?ssler system be obtained.Finally,the correctness and validity of the conclusion were verified by simulating the fractional R?ssler system.3)The control problem of feedback linearization for a class of nonlinear fractional systems was investigated.Firstly,based on the Lyapunov stability theorem,the stability condition of nonlinear fractional order system and the design of feedback controller were discussed by feedback linearization.Secondly,the stability condition for the fractional order loss type of the modified coupled dynamos system is stabilized at different.Finally,the correctness and validity of the conclusion were verified by simulating the fractional loss type of the modified coupled dynamos system.