On The Bound And Existence Of The Hermitian Positive Defnite Solutions Of The Nonlinear Matrix Equation X^s+A*X^-tA=Q

Matrix equation is widely applied in control theory, statistics, stochastic fl-tering, dynamic programming, queueing theory and ladder networks. At present,the research of matrix equation has been the hot pot for scholars.In this paper, we improve the bound and derive new sufcient conditionsof the existence and uniqueness of the hermitian positive defnite solution of thenonlinear matrix equation X^s+A*X^-tA=Q. This paper mainly contains threechapters:In chapter one, frstly, the applied background and some recent results ofthis nonlinear matrix equation will be introduced. Secondly, the main work ofthis paper will be introduced. Thirdly, the notations used in this paper will belisted.In chapter two, by utilizing the relationship between this nonlinear matrixequation and continuity of real function, and combing the knowledge of matrixinequalities, Schur Complement and continuity principle of real functions, newbound of the hermitian positive defnite solution of this matrix equation is es-timated, which improve the recent results. Its superiority will be showed bynumerical examples.In chapter three, new sufcient conditions of the existences and uniquenessof the hermitian positive defnite solution of this nonlinear matrix equation isderived by utilizing the new bound of the hermitian positive defnite solution ofchapter two, the fxed-point theorem, matrix inequalities, and properties of ma-trix norm. Further more, based on some spacial conditions, the existences anduniqueness conditions of the hermitian positive defnite solution of this nonlin-ear matrix equation is extended by using the relationship between integral andrational numbers. Its superiority will be showed by numerical examples.