Stability Of Nonlinear Systems And Networked Games Research Via Semi-tensor Product

The semi-tensor product of matrices is a new mathematical tool proposed by Chinese scholars,which not only overcomes the limitation of the common multiplication of the matrix,but also retains most of the properties of matrix multiplication,and the semi-tensor product method has a broad application prospect.This paper mainly studies the stability of nonlinear systems and networked games via semi-tensor product mothed,the paper is divided into four chapters:In chapter 1,the development and research status of semi-tensor product are introduced,stability of nonlinear systems and networked games,some basic knowledge and preparatory theory are introduced.In chapter 2,general polynomial nonlinear systems are represented as the matrix via semi-tensor product method,a Lyapunov function is constructed by this form,a theorem of judging whether a class of nonlinear systems are asymptotically stable is proved through semi-tensor product method.In chapter 3,an algebraic formulation of the networked game under a class of rules is established via semi-tensor product,a necessary and sufficient theorem for the game globally converges to the optimal strategy is found,the time needed for the game converges to the optimal strategy combination is found.In chapter 4,an algebraic formulation of networked game with different strategies is established via semi-tensor product,a theorem for the game globally converges to the optimal strategy is found,the game globally converges to the optimal strategy combination is proved.Chapter 5 is a summary of paper.