摄动连续Riccati矩阵方程解矩阵界的估计  

Estimation of Solution Matrix of Perturbed Continuous Riccati Matrix Equation

作　　者：王春[1] 

机构地区：[1]黑龙江科技学院理学院,哈尔滨150027

出　　处：《科技导报》2010年第19期59-61,共3页Science & Technology Review

基　　金：黑龙江省教育厅科学技术研究项目(11544048)

摘　　要：Riccati矩阵方程在控制理论和状态估计问题的研究中具有重要的理论和实用价值。针对摄动参数为带有范数有界不确定性的摄动连续Riccati矩阵方程解矩阵界估计问题,通过构造两个半正定矩阵,利用矩阵不等式和特征值的性质得到带有范数有界不确定性的摄动连续Riccati矩阵方程解矩阵新的上下界,利用特征值满足的不等式给出解矩阵特征值新的上下界。这些上下界的计算只涉及矩阵特征值的计算和线性矩阵不等式的求解,上下界的估计均由矩阵不等式给出,避免了高阶代数方程的求解。数值算例验证表明,研究结果是可行的。The Riccati matrix equation has a theoretical and practical importance in the control theory and the state estimation problems.The estimation of the solution matrix of the perturbed continuous Riccati matrix equation is studied in this paper.The perturbation parameters of this equation are of norm-bounded uncertainty.The new upper and lower bounds of the solution matrix for the perturbed continuous Riccati matrix equation are derived by constructing two semi-definite matrices,using matrix inequalities and characteristics of eigenvalues of the matrices.The calculations of upper and lower bounds require only the eigenvalues of the matrices and the solution of linear matrix inequalities.All estimations of bounds are given by matrix inequalities.Thus one does not have to solve the higher-order equation.The results obtained are verified by a numerical example,and the feasibility is illustrated.

关 键 词：摄动连续Riccati矩阵方程 范数有界不确定性 解矩阵 

分 类 号：O231[理学—运筹学与控制论]