Existence And Uniqueness Analysis And Inversion-free Iterative Algorithm For Symmetric Positive Definite Solutions Of A Class Of Discrete-coupled Riccati Matrix Equations

In the study of control systems,the stability,controllability and observability of the system are several important aspects to solve theoretical and practical problems.In many cases,the study of these problems can often be transformed into the upper and lower bounds of the semipositive definite solution or semipositive definite solution of the corresponding Riccati matrix equation.In recent years,the iterative algorithm for the upper and lower bounds estimation and solution of the semi-positive definite solution of algebraic Riccati matrix equation has received great attention from many scholars,and some important research results have been obtained.In this paper,we obtain the existence interval of discrete coupled Riccati matrix equation(DCARE)symmetric semidefinite solution,the uniqueness condition of semipositive definite solution and the inversion-free iterative algorithm of semidefinite solution.The details are as follows:In the first chapter,briefly introduces the application background,research significance and recent work of the discrete coupled Riccati matrix equation,and explains the basic notation used in this paper.In the second chapter,the original discrete coupled Riccati matrix equation(DCARE)is transformed into another form of discrete coupled Riccati matrix equation(DCARE)using the properties of matrix identity,inverse matrix and matrix Schur complement.Furthermore,using the matrix eigenvalue property,matrix inequality,and the relationship between the root and coefficient of the quadratic equation,the existence interval of the DCARE semidefinite solution is obtained.The uniqueness condition of the semipositive definite solution is given by using the matrix inequality and the fixed point principle.Finally,numerical examples are given to illustrate the validity of the theorem.In the third chapter,using the existence interval and the uniqueness condition of the semi-positive definite solution of the semi-positive definite solution of the discrete coupled Riccati matrix equation obtained in Chapter 2,two iterative algorithms for avoiding the inverse operation are given,and its convergence and error are discussed.