Trace Inequalities for Matrix Products and Trace Bounds for the Solution of the Algebraic Riccati Equations
نویسندگان
چکیده
By using diagonalizable matrix decomposition and majorization inequalities, we propose new trace bounds for the product of two real square matrices in which one is diagonalizable. These bounds improve and extend the previous results. Furthermore, we give some trace bounds for the solution of the algebraic Riccati equations, which improve some of the previous results under certain conditions. Finally, numerical examples have illustrated that our results are effective and superior.
منابع مشابه
Analytical and Verified Numerical Results Concerning Interval Continuous-time Algebraic Riccati Equations
This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...
متن کاملLower bounds on the solution of coupled algebraic Riccati equation
Upper bounds for eigenvalues of a solution to continuous time coupled algebraic Riccati equation (CCARE) and discrete time coupled algebraic Riccati equation (DCARE) are developed as special cases of bounds for the uni...ed coupled algebraic Riccati equation (UCARE). They include bounds of the maximal eigenvalues, the sums of the eigenvalues and the trace.
متن کاملEla a New Upper Bound for the Eigenvalues of the Continuous Algebraic Riccati Equation
By using majorization inequalities, we propose a new upper bound for summations of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation. The bound extends some of the previous results under certain conditions. Finally, we give a numerical example to illustrate the effectiveness of our results.
متن کاملEla New Lower Solution Bounds for the Continuous Algebraic Riccati Equation
In this paper, by constructing the equivalent form of the continuous algebraic Riccati equation (CARE) and applying some matrix inequalities, a new lower bounds solution of the CARE is proposed. Finally, corresponding numerical examples are provided to illustrate the effectiveness of the results.
متن کاملNew lower solution bounds for the continuous algebraic Riccati equation
In this paper, by constructing the equivalent form of the continuous algebraic Riccati equation (CARE) and applying some matrix inequalities, a new lower bounds solution of the CARE is proposed. Finally, corresponding numerical examples are provided to illustrate the effectiveness of the results.
متن کامل