Stability Analysis And Controller Design For Fractional Order Nonlinear Singular Systems

Fractional order calculus is a field of study in mathematics,which is an extension of integer order calculus,which can describe the physical system in life more accurately than the integer order.In most reality physical system,there are usually many nonlinear structures.Therefore,the stability and stabilization analysis of fractional order nonlinear systems are great significance.At present,the effective stability analysis and controller design method are still lacking for normal fractional order nonlinear systems.This paper mainly studies fractional order nonlinear system and fractional order nonlinear singular system.For fractional order nonlinear systems,the stability and the stabilization of the systems are discussed by using the Lyapunov direct method.On this basis,the robust stability and robust stabilization of the fractional nonlinear uncertain system are studied.For fractional order nonlinear singular systems,the new stability criterion and stabilization controller design method are given by using equivalent transformation and solving solution method.The specific research contents of this paper are as follows:(1)The background,theoretical development and research status of fractional order nonlinear systems and fractional order nonlinear singular systems are introduced.The basic knowledge of fractional order calculus and the general functions are briefly introduced.(2)By using the Lyapunov direct method and comparison principle,the stability of fractional order nonlinear system is studied and the stability criterion of fractional order nonlinear system is given.Then,based on the above theorem,the controller design problem of fractional order nonlinear system is studied,and the controller design method of fractional order nonlinear system is given.(3)Using the Lyapunov direct method and comparison principle,the fractional order nonlinear uncertain systems is studied in the robust stability and robust stabilization problems,gives the robust stability theory and robust stabilization controller design of the parameter uncertainty fractional order nonlinear systems;Based on the linear matrix inequality(LMI)and matrix singular value decomposition method,the fractional order nonlinear uncertain systems are studied,the design of observer-based state feedback controller of the fractional order nonlinear uncertain systems was given.(4)Using equivalent transformation and the analytic solution method,through the slow subsystem to determine the change of the fast subsystem,the stability and stabilization of the fractional order nonlinear singular system is studied,gives a fractional order nonlinear singular system stability theorem and stabilization of the controller design.(5)Using the LMI toolbox in MATLAB to solve the linear matrix inequality in the calculation example,the system simulation images are drawn by the Simulink toolbox in MATLAB to verify the validity of the relevant conclusions.