No abstract

By utilizing some linear algebraic techniques, new upper bounds of the solution of the continuous algebraic Riccati equation (CARE) are derived. According to the present bounds, iterative procedures are also developed for obtaining more precise estimations. Comparing with existing results, the obtained bounds are less restrictive.

Matrix bounds of the solutions of the continuous and discrete Riccati equations-a unified approach CHIEN-HUA LEE{In this paper, a new scheme is introduced to measure the matrix bounds of the continuous and discrete Riccati equations. By estimating upper and lower matrix bounds of the solution of the unified algebraic Riccati equation (UARE), the same measurements for the solutions of the continuous and discrete Riccati equations, respectively, can be obtained in limiting cases. According to these obtained matrix bounds, several eigenvalue bounds are also defined. All the proposed results for the UARE are new and more general than previous work. Some obtained results are compared with those of the literature. Via numerical examples, it is shown that in some cases the presented results are tighter than the existing ones.

Upper and lower bounds of the solutions of the discrete algebraic Riccati and Lyapunov matrix equationsCHIEN-HUA LEE² Matrix bounds, upper and lower, for the solution of the discrete algebraic Riccati and Lyapunov equations respectively, are proposed in this paper. They are new or sharper than the majority of existing results. By making use of these new matrix bounds, the corresponding bounds for each eigenvalue, the trace and the determinant of these solution matrices are also presented. Comparisons are made between these bounds and the majority of those appearing in the literature. It is shown that the obtained results are tighter. Finally, we give illustrative examples to show that these estimates appear to be considerably stronger than previously available results in many cases. Notation real number ® eld A Â transpose of a matrix A Î n´m |a| the absolute value of a complex number a i ( A) the i th eigenvalue of A Î n´n , all of |¸i ( A) | are arranged in nonincreasing order, i.e. |¸1 ( A) | |¸2 ( A) | ´´´ |¸n ( A) | If A is symmetric, then all of¸i( A) are arranged in non-increasing order, i.e.¸1 ( A) ¸2( A) ´´´ ¸n( A) s i ( A) the i th singular value of A Î n´m , the values of s i (X) are arranged in non-increasing order, i.e. s 1 ( A) s 2 (A) ´´´ s n ( A) tr ( A) the trace of matrix A Î n´n det ( A) the determinant A Î n´n

On the estimation of solution bounds of the generalized Lyapunov equations and the robust root clustering for the linear perturbed systems CHIEN-HUA LEE{ and SU-TSUNG LEE{This paper measures the solution bounds for the generalized Lyapunov equations (GLE). By making use of linear algebraic techniques, we estimate the upper and lower matrix bounds for the solutions of the above equations. All the proposed bounds are new, and it is also shown that the majority of existing bounds are the special cases of these results. Furthermore, according to these bounds, the problem of robust root clustering in sub-regions of the complex plane for linear time-invariant systems subjected to parameter perturbations is solved. The tolerance perturbation bounds for robust clustering in the given sub-regions are estimated. Compared to previous results, the feature of these tolerance bounds is that they are independent of the solution of the GLE.