Solution Bounds For The Discrete And Continuous Algebraic Riccati Matrix Equations

Algebraice Riccati equations is usually encountered in the modern controlsystem, numerical algebra and diferential equations and so on.The research ofsolving the algebraice Riccati equations not only can develop the matrix theorybut also can provide the theoretical and practical basis. Thus, the theory hashigh value and practical significance.In this paper,by constructing a matrix identity and utilizing eigenvalue in-equalities, singular value inequalities, linear algebra skills and so on, we shall givelower and upper bound estimates of solution matrix of algebraic Riccati equationwhen algebraic Riccati equation have positive semi-definite solution.Then, weshall give numerical examples to demonstrate the efectiveness of the proposedresults, making comparisons with the existing results.Main contents as follows:In chapter one, we first introduce some background knowledge and recentworks for the discrete algebraic Riccati equations. Then we proposed the mainwork and give some basic natations and definitions used in our thesis.In chapter two, by utilizing Sherman-Morrison-Woodbury formula,we firstgive the equivalent form of the algebraic Riccati equation; Second,according tothe equivalent forms, by constructing a identical equation and utilizing Courant-Fisher inequality!Weyl inequalities and linear algebra techniques,we then derivesome new lower bound of the discrete algebraic Riccati equation solution matrix.Finally, we give numerical examples to demonstrate the efectiveness of the pro-posed results, making comparisons with existing results.In chapter three, first, by constructing a series of matrix identical equationand utilizing the control inequality of matrix, matrix inequality as well as someof the results which was obtained, we derive some of new upper and lower boundsof solution matrix of continuous algebraic Riccati equation.Second new boundare proposed, which can be used to derive tighter upper matrix bounds. Finally,we give numerical examples to demonstrate these concept that the results whichwe obtain are not mutually contain,...