The Estimation Of Solution To The Continuous Coupled Algebraic Riccati Matrix Equation

In automatic control, solid mechanics and parameter identification fields,a lot of theory and practical problems usually can be changed into researching related matrix equations and related matrix properties. In the control system, the system of optimal control and the stability of the system attract great at-tention.Many problems can be summed up in solving Riccati matrix equations and estimating the upper and lower solution bounds.Therefore,many scholars pay much attention to the property of the continuous coupled algebraic riccati matrix equation and achieve results.Basing on the condition that the continuous coupled algebraic Riccati matrix equation(CCARE) has only one symmetric positive definite solution,we estimate the upper and lower solution bounds which extend previous work and demon-strate the effectiveness through corresponding numerical examples.Main contents as follows:In chapter one, some background knowledge for the continuous coupled al-gebraic Riccati matrix equations, and some basic symbols with definitions are introduced in this paper.In chapter two,by investigating the characteristics of the coefficient matrix that is the Riccati matrix equation and the properties of positive definite matrices, we construct the positive definite matrices which relate to matrix equations,and establish matrix inequalities combining limite thinking.Then we get the equivalen-t form of the continuous coupled algebraic Riccati matrix equation(CCARE) by matrix transformation.More by combining the property of M matrix with control of inequations,eigenvalues inequations and inequality techniques,we solve matrix inequalities to establish the bounds of the largest eigenvalue,then we derive the estimating of the new upper solution bounds which improve and extend some resent results.Further,this thesis proposes iterative algorithms to obtain tighter upper matrix bounds of the CCARE,and a example to show the advantages of the derived results.In chapter three, on the basis of the the bounds of the largest eigenvalue which established in chapter tow,by using the properties of M-matrix and nonneg-ative matrix again,we obtain the new lower solutions bounds of CCARE. Examples explain the effectiveness.