摄动离散矩阵Lyapunov方程解的估计

On the estimation of solutions to perturbed discrete matrix Lvapunov equations

研究摄动离散矩阵Lyapunov方程解的估计问题,利用矩阵运算性质及Lyapunov稳定性理论,给出在结构不确定性假设下方程解的存在条件及解的上下界估计,估计结果由一个线性矩阵不等式(LMI)和两个矩阵代数Riccati方程确定．针对几种不确定性假设,进一步给出矩阵代数Riccati方程的具体形式．最后通过一个算例说明了所得结果的有效性．

The estimation of the solution to the perturbed discrete matrix Lyapunov equation is stuclled, lne existence condition and upper and lower bounds estimation of the solution to the equation under the structured uncertainty assumption are presented by applying the operational property of matrix and Lyapunov stability theory, the estimation is then determined by a linear matrix inequality （LMI） and two matrix algebra Riccati equations. The concrete form of matrix algebra Riccati equations are also given for some uncertainty assumptions. Finally, the effectiveness of above results is shown by an example.