The Solution Bounds Of The Continuous Algebraic Riccati Matrix Equation And Its Application In Redundant Problem

There are many fields are involved in the design,control and optimization of the control system,such as,biological engineering,spacecraft control and so on.In the design of these control systems,its controllability,observability and stability need to consider.However,these problems often can be converted into solving the solution,estimating the upper and lower solution bounds and the property of the solution of the corresponding Riccati equation.Therefore,many scholars have carried on the exploration to solving Riccati matrix equation and many research results have been obtained.Firstly,we derive two new upper bounds of the continuous algebraic Riccati matrix equation basing on special matrix,the inequality of matrix eigenvalue,the identity transformation of matrix and the properties of solution for the continu-ous algebraic Riccati matrix equation.Secondly,we study some specific applications about the solution of the continuous algebraic Riccati matrix equation in the re-dundant problem.Main contents of this paper as follows:In chapter one,we mainly introduce the application background,source and recent work of continuous algebraic Riccati matrix equation,and introduce some basic symbols used in this paper.In chapter two,according to the properties of the equation given matrix,we construct a new semi-positive definite matrix.Basing on some significant prop-erties of the matrix eigenvalue and eigenvalue inequality,using inequality tech-niques and formula transformation,combining the new semi-positive matrix,two new upper bounds of the continuous algebraic Riccati matrix equation are ob-tained.Further,we show the effectiveness of the results by numerical examples.In chapter three,basing on the previous results and the important property of the matrix eigenvalue and singular value,by inequality techniques,we present some new sufficient conditions to ensure the decrease of controller gain when increasing the control input.Moreover,we show the effectiveness of the results by the numerical example,respectively.