Stability Analysis And Control Of Nabla Discrete Fractional-order Nonlinear Systems

Compared with integer-order systems,fractional-order systems are used for a better description of the natural phenomena and a better simulation of the physical phenomena and dynamic processes with memory or non-locality.With the rapid development of digital computers in recent years,increasing numbers of scholars are paying more attention to the study of discrete fractional-order systems,as most real systems run in discrete time series.Therefore,we mainly study the dynamical properties of nabla discrete fractionalorder nonlinear systems.The main contents are as follows:In Charpter 1,the research background and analysis of the current research situation of this thesis are presented,and the preliminary knowledge is given related to this thesis.In Chapter 2,the stability analysis of nabla discrete fractional-order nonlinear systems and the design method of state feedback controllers are studied.Firstly,a sufficient condition of Mittag-Leffler stability for a class of nabla discrete fractional-order nonlinear systems is given in the form of linear matrix inequality.Secondly,based on stability analysis,the existence conditions and design methods of state feedback controllers for nabla discrete fractional-order nonlinear systems are presented.Finally,numerical examples are provided to verify the validity of the results.In Chapter 3,we mainly study the design of the observer for a class of nabla discrete fractional-order nonlinear systems.For a class of nabla discrete fractional-order nonlinear systems,considering the conditions of Lipschitz,one-sided Lipschitz and quasi-one-sided Lipschitz are satisfied,the existence condition and design method of the observer are given,and verified with numerical examples.In Chapter 4,the stability of the nabla discrete distributed-order nonlinear systems is investigated.Firstly,some properties of the nabla discrete distributed-order operators are derived.Secondly,a sufficient condition for the asymptotic stability of the nabla discrete distributed-order nonlinear systems is proposed based on Lyapunov direct method.In addition,based on these properties,a simpler criterion is provided to determine the stability of such systems.Finally,some examples are given to illustrate the validity of these results.Finally,the main work of this thesis is summarized and the future work is prospected.