Research On Stability Analysis And Feedback Control Of Nonlinear Systems

In practical dynamic systems,almost all systems are nonlinear,so the control problem of nonlinear systems is a more and more popular topic,in which linear systems are a simplification of nonlinear systems.Although the research of nonlinear system has been a lot of achievements,but because of its complexity,still need further exploration,the key research content is feedback control which adapts to nonlinear systems with special structure.1)The problem of predictive feedback control design for nonlinear fractional order systems was studied.Firstly,based on the Lyapunov stability theorem,sufficient conditions of the stability for nonlinear fractional order systems were obtained via predictive feedback control.Secondly,by using the singular value decomposition(SVD)method,the sufficient conditions were linearized,and a linear matrix inequality(LMI)was obtained.Finally,the Lorenz fractional order system and the nonlinear fractional system were simulated respectively,and the effectiveness of the proposed method was verified.2)The generalized projective synchronization based on feedback control for nonlinear chaotic fractional order(0(27)?(27)2)dynamical systems was investigated.Firstly,based on the stability theorem of fractional order linear system,the feedback controller design of chaotic fractional order system was obtained by using the new generalized projective synchronization scheme.Secondly,the error system is obtained by using the designed synchronization scheme and feedback controller,and the stability of the system was proved,and the control and synchronization of the master-slave chaotic fractional order system were realized.Finally,the Newton-Leipnik,R?ssler,Chua's systems were simulated,verify the effectiveness of the proposed method.3)The fault tolerant control of nonlinear time-delay singular systems based on fault diagnosis was researched.Firstly,a new fault diagnosis observer is designed by describing nonlinear time-delay singular systems,and the state estimation error of the constructed fault diagnosis observer were explored,by using Lyapunov stability theory,the sufficient conditions for stability of the system are obtained in term of LMI.Secondly,the state feedback fault-tolerant controller is constructed,and the sufficient conditions for the stability of system are obtained in term of LMI by applying the Lyapunov stability theory,the condition that the closed-loop system is stable and satisfies a given)93(_?performance index was studied.Finally,the effectiveness of the proposed method was verified by simulation of the nonlinear time-delay singular system extended by Lorenz systems.