Estimating Domains Of Attraction Of Autonomous Nonlinear Systems

This thesis is devoted to studying estimation of the domain of attraction (DOA) of autonomous nonlinear systems. Three methods are introduced for it. Importantly, the stability and DOA of a class of SIRS epidemic model are studied and the DOA of a class of quadratic polynomial system with parameters is estimated on the basis of former results. It consists of seven chapters.In chapter 1, the background and present conditions of estimation of DOA of autonomo-us nonlinear systems are introduced briefly.In chapter 2, the moment problem, moment matrix, stability definitions and theorems in the Lyapunov sense, the definition of DOA, and the estimation of DOA as an optimization problem are introduced.In chapter 3, some important results about polynomial minimum problem are introduced A LMI (linear matrix inequality) optimization algorithm to compute the DOA based on the theory of moments is given. In the end, a corresponding example is given.In chapter 4, some definitions and theorems about maximal Lyapunov functions are intr-oduced. What's more, another method-recursive algorithm of rational polynomials is given. It is illustrated with an example.In chapter 5, the third method-parameterization for polynomial systems is introduced. And the DOA of a class of quadratic system with parameters is studied.In chapter 6, the stability and DOA of a class of SIRS epidemic model with immigrants of constant for population with varying size are studied.In the last chapter, the whole paper is summed up and the problems which are still unsolved in the research are showed.