The Two Parametric Upper Bound For The Solution Of The Continuous Algebraic Riccati Matrix Equation And Its Application

The stability,controllability and observability of the system are three impor-tant characteristics of modern control system.In many cases,researching these characteristics can be converted into researching the positive semi-definite solution or solution bounds of the algebraic Riccati matrix equation.Therefore,in recent years,experts and scholars have been focused on the solution bound of the alge-braic Riccati matrix equation and its appliation,and obtained plenty of research results.In this paper,by utilizing the properties of particular matrix,matrix inequal-ities and other linear algebraic techniques,we get a new two parametric upper bound for the solution of the continuous algebraic Riccati matrix equation,and apply it to the problem of redundant optimal control.Specific contents as follows:In chapter one,we briefly introduce the application background,research sig-nificance and recent studies of algebraic Riccati matrix equation,and introduce some marks with definitions used in the paper.In chapter two,by using the properties of continuous algebraic Riccati ma-trix equation given matrix and constraint conditions,we constract the related positive semi-definite matrix.Then,using constructed matrix and its properties,matrix inequalities,matrix eigenvalue inequalities and inequality techniques,a new two parametric upper solution bound of the equation is derived.Further,the monotonicity of the upper bound of one parameter is proved,which illuminates it improves some previous related results.Finally,we give examples to show its effectiveness and superiority.In chapter three,in the problem of redundant optimal control,we use the upper solution bound of the continuous algebraic Riccati matrix equation derived in the second chapter,matrix trace inequalities,matrix eigenvalue inequalities and the properties of matrix spectrum norm to obtain two sufficient conditions to ensure that the controller gain is reduced as the control input is increased,and we give examples to show their effectiveness.