共查询到20条相似文献,搜索用时 31 毫秒
1.
In recent years, several eigenvalues, norms and determinants bounds have been investigated separately for the solutions of continuous and discrete Riccati equations. In this paper, an upper bound for solution of the unified Riccati equation is presented. In the limiting cases, the result reduces to a new upper bound for the solution of continuous and discrete Riccati equation. 相似文献
2.
In this paper, we propose upper bounds for the sum of the maximal eigenvalues of the solutions of the continuous coupled algebraic Riccati equation (CCARE) and the discrete coupled algebraic Riccati equation (DCARE), which are then used to infer upper bounds for the maximal eigenvalues of the solutions of each Riccati equation. By utilizing the upper bounds for the maximal eigenvalues of each equation, we then derive upper matrix bounds for the solutions of the CCARE and DCARE. Following the development of each bound, an iterative algorithm is proposed which can be used to derive tighter upper matrix bounds. Finally, we give numerical examples to demonstrate the effectiveness of the proposed results, making comparisons with existing results. 相似文献
3.
JÜRGEN GARLOFF 《International journal of control》2013,86(2):423-431
We present some bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the discrete Riccati and Lyapunov matrix equations and the continuous Lyapunov matrix equation. Nearly all of our bounds for the discrete Riccati equation are new. The bounds for the discrete and continuous Lyapunov equations give a completion of some known bounds for the extremal eigenvalues and the determinant and the trace of the solution of the respective equation. 相似文献
4.
In recent years, several bounds have been reported for the solution of the continuous and the discrete Lyapunov equations. Using the unified Lyapunov equation, we give in this paper bounds for the solution of this equation. In the limiting cases, the bounds reduce to existing bounds for both the continuous and discrete Lyapunov equations. 相似文献
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6.
Juan Zhang 《Asian journal of control》2014,16(1):284-291
In this paper, applying majorization inequalities, new upper and lower bounds for summation of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation are presented. Corresponding numerical examples illustrate that our new bounds extend some of the recent results. 相似文献
7.
Chien-Hua Lee 《International journal of control》2013,86(6):635-642
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. 相似文献
8.
Upper bounds for individual eigenvalues and for summations of eigenvalues including the trace of the solution of the discrete algebraic Riccati equation are presented. Some are new, and some supplement bounds in the literature 相似文献
9.
By using singular value decomposition and majorisation inequalities, we propose new upper and lower bounds for summations of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation. These bounds improve and extend some of the previous results. Finally, we give corresponding numerical examples to illustrate the effectiveness of our results. 相似文献
10.
This paper provides new lower and upper matrix bounds of the solution to the discrete algebraic Riccati equation. The lower bound always works if the solution exists. The upper bounds are presented in terms of the solution of the discrete Lyapunov equation and its upper matrix bound. The upper bounds are always calculated if the solution of the Lyapunov equation exists. A numerical example shows that the new bounds are tighter than previous results in many cases. 相似文献
11.
Simultaneous eigenvalue bounds for the solution of the unified non-stationary Lyapunov matrix equation are presented. When the solution becomes stationary, the results reduce to bounds of the unified type algebraic Lyapunov equation. In the limiting cases, the results reduce to bounds for the solution of the differential and difference Lyapunov equations. The bounds given in this paper are a generalization of some existing bounds obtained separately for the continuous and discrete type stationary and non-stationary Lyapunov equations. 相似文献
12.
Summation bounds for the eigenvalues of A'P+PA are presented. Here matrices A,P∈Rn×n, P is positive definite and A'=transpose of A. These bounds are employed to derive new upper bounds for summations of eigenvalues of the solution of the continuous algebraic Riccati equation 相似文献
13.
Chien-Hua Lee 《Automatic Control, IEEE Transactions on》1997,42(9):1268-1271
New upper bounds for the solution eigenvalues of the continuous algebraic matrix Riccati equation are developed. They include bounds of the extreme eigenvalues, the summation and product of eigenvalues, the trace, and the determinant. It is shown that the majority of the present eigenvalue bounds, expressed in concise forms, are less restrictive and sharper than existing results 相似文献
14.
Chien-Hua Lee 《Automatic Control, IEEE Transactions on》1997,42(6):840-842
A new upper matrix bound of the solution for the discrete algebraic matrix Riccati equation is developed. This matrix bound is then used to derive bounds on the eigenvalues, trace, and determinant of the same solution. It is shown that these eigenvalue bounds are less restrictive than previous results 相似文献
15.
ENGIN YAZ 《International journal of systems science》2013,44(7):815-820
Novel bounds are proposed for the extreme and lower half eigenvalues of the solution matrix for the algebraic Riccati equation. The formulae giving these bounds can easily be applied to determine the region where the eigenvalues lie, and the bounds have the added advantage of being sharper in some cases than the previously proposed ones, as some realistic examples will show. The proposed bounds find many applications which are pointed out in the text. 相似文献
16.
讨论摄动离散Riccati方程正定解的估计问题。针对摄动参数满足范数有界不确定性情形,获得了正定解的上界和下界,且界的计算通过确定的离散Riccati方程的解给出,避免高阶代数方程的求解,同时得到基于Riccati方程的摄动离散系统稳定性分析的新方法,所给出的数值算例验证了方法的可行性。 相似文献
17.
Bounds on extremal eigenvalues and lower and upper bounds of the trace for the solution of the algebraic Riccati equation are presented. Through two examples, it is shown that, in some special cases, the presented bounds can be better than the results recently published 相似文献
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19.
In this note various lower bounds for all the eigenvalues of the solution matrixK of the Lyapunov matrix equation are established. A special case of this result is a generalization of that presented in [1]-[3], where lower bounds for the maximum and minimum eigenvalues ofK are given. Moreover, the approach used here enables one to establish various lower bounds for some of the (largest) eigenvalues of the solution matrix of the algebraic Riccati equation. 相似文献
20.
Wei Xing Qingling Zhang Qiyi Wang 《Automatic Control, IEEE Transactions on》2000,45(8):1563-1569
Estimates of bounds on the solutions of Lyapunov and Riccati equations are important for analysis and synthesis of linear systems. In this paper, we propose new trace bounds for the product of two general matrices. The key point for removing the restriction of symmetry is to replace eigenvalues partly by singular values in the equation of bounds. The results obtained are valid for both symmetric and nonsymmetric cases and give tighter bounds in certain cases 相似文献