摘要
利用矩阵求逆公式,推导出一般离散时间代数R iccati方程的等价形式,给出其对称正定解矩阵P的上、下界及其极特征值的上、下界;利用Rayleigh不等式及矩阵特征值的性质,获得了解矩阵P的几个更紧凑的上、下界.黑龙江省所得结果为标准离散时间代数R iccati方程相应结果的推广.数值算例表明了所用方法的有效性.
In this paper, by using the formula of matrix inversion an equivalent form of the general discrete time algebraic Riccati equation isproposed, the upper and lower matrix bounds and the extreme eigenvalue bounds of the symmetric positive definite solution matrix P are also given. Then, some tighter upper and lower matrix bounds for the solution matrix P are obtained. By applying Reyleigh inequality and the properties of matrix eigenvalue. Our results are the generalization of those about standard discrete time algebraic Riccati equation. The proposed results are illustrated through a numerical example.
出处
《哈尔滨理工大学学报》
CAS
2005年第6期28-31,34,共5页
Journal of Harbin University of Science and Technology
基金
国家自然科学基金项目(10471031)
