The Existence of the Solution to One Kind of Algebraic Riccati Equation

3rd International Conference on Energy Equipment Science and Engineering

Liu, Jianming^1

Quanzhou Normal University, Quanzhou

362000, China^1

关键词: Algebraic Riccati equations;    Arbitrary constants;    Contraction mappings;    Engineering applications;    Fixed point theorems;    Functional approach;    Negative semi-definite;    Symmetric matrices;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/128/1/012129/pdf
DOI  :  10.1088/1755-1315/128/1/012129

来源: IOP

【 摘 要 】

The matrix equation ATX + XA + XRX + Q = O is called algebraic Riccati equation, which is very important in the fields of automatic control and other engineering applications. Many researchers have studied the solutions to various algebraic Riccati equations and most of them mainly applied the matrix methods, while few used the functional analysis theories. This paper mainly studies the existence of the solution to the following kind of algebraic Riccati equation from the functional view point: ATX + XA + XRX -λX + Q = O Here, X, A, R, Q ∈n×n, Q is a symmetric matrix, and R is a positive or negative semi-definite matrix, λ is arbitrary constants. This paper uses functional approach such as fixed point theorem and contraction mapping thinking so as to provide two sufficient conditions for the solvability about this kind of Riccati equation and to arrive at some relevant conclusions.