The Perturbation Estimates Of Solution To The Coupled Algebraic Riccati Matrix Equations

In solid mechanics,parameter identification and automatic control fields,some theory and practical problems can often be converted into studying related matrix properties and related matrix equations.In optimal control field,some problems reduce to discussing solving the solution and the solution properties of the rel-ative algebraic Riccati matrix equations.This thesis discusses the perturbation solution of the coupled algebraic Riccati matrix equations in control system.This thesis firstly shows the perturbation estimates of the solution for the discrete algebraic Riccati matrix equation and the perturbation estimates of the solution for the continuous algebraic Riccati matrix equation.In chapter one, some background knowledge for the continuous coupled alge-braic Riccati matrix equations and the discrete coupled algebraic Riccati matrix equations, and some basic symbols with definitions are introduced in this paper.In chapter two,if the discrete coupled algebraic Riccati matrix equation and its perturbation equation exist position definite solutions,we discuss the pertur-bation bounds of the positive definite solution by applying the derived upper and lower bounds,combining with the property of matrix norm. Moreover, by using majorization inequalities and classical eigenvalue inequalities, combining inequality techniques, we get the perturbation estimates of the solution for the discrete algebraic Riccati matrix equation, new upper matrix bounds of the solu-tion for the perturbed discrete coupled algebraic Riccati equation(DCARE) are established by using some classical matrix identities to construct the equivalent form of this equation,utilizing the properties of M-matrix, Finally, numerical example illustrate the effectiveness.In chapter three, upper matrix bounds of the solution for the perturbed continuous coupled algebraic Riccati equation(CCARE) are established by using some classical matrix identities to construct the equivalent form of this equation, utilizing the properties of M-matrix and nonnegative matrix to solve linear in-equalities. Moreover, this thesis proposes iterative algorithms to obtain tighter upper matrix bounds of the solution for the perturbed continuous coupled algebra-ic Riccati equation(CCARE). Finally, numerical example shows the effectiveness of the derived result.