New Upper Bound For The Solution Of The Continuous Coupled Algebraic Riccati Matrix Equation And Its Application In A Class Of Time-delay Systems

With the fast growth and quickly development of modern science and technology,many researchers has been paid attention to the system of control.Three vital characteristics of the modern system of control is the system's stability,controllability and observability,and in many practical problems,the study of this nature can be converted into the corresponding Riccati matrix equation of the properties of positive semi-definite solutions for research.However,so far there is no general theoretical method to solve the positive semi-definite solution of Riccati matrix equation effectively,and we only need to discuss the estimation of the bounds of its solutions in many practical matters.Therefore,for the past few years,many learned men are apt to study the estimation of upper and lower bound of Riccati matrix equation and its application,and a lot of conclusions have been got.This paper mainly concentrates on the estimation of the upper bound of the solution of the continuous coupled algebraic Riccati matrix equation corresponding to the coupled system,and then researches the stability of a class of delay systems.In this paper,on the grounds of the constraint conditions and the structure of the continuous coupled algebraic Riccati matrix equation,we develop a positive semidefinite matrix by means of the method of continuous transition.In combination with singular value decomposition and contract transformation,the continuous coupled algebraic Riccati matrix equation is deformed.Secondly,recur to sufficient and necessary conditions for the real part of the matrix to be positive definite and the characters of the matrix equation,the matrix inequalities about the solutions are gained.Then,in the light of the operational properties of the 9)0)(86)0) product and the characteristic of the -matrix and the nonnegative property of its inverse matrix,we get the upper bound of the positive semi-definite solution of the continuous coupled algebraic Riccati matrix equations,ameliorated the recent number of existing conclusions,and the specific numerical example testifies its feasibility,practicability and superiority of our approach.Finally,the paper chooses the Lyapunov function as the (1 function by taking advantage of the positive definiteness of the solution of the continuous coupled algebraic Riccati matrix equation,and acquires the stability conditions for a class of time-delay systems by utilizing some matrix correlation inequalities and Lyapunov stability theory.