基于Delta算子的统一代数Lyapunov方程解的上下界

Matrix bounds for the solution of the unified algebraic Lyapunov equation using Delta operator

基于Delta算子描述,统一研究了连续代数Lyapunov方程(CALE)和离散代数Lyapunov方程(DALE)的定界估计问题.采用矩阵不等式方法,给出了统一的代数Lyapunov方程(UALE)解矩阵的上下界估计,在极限情形下可分别得到CALE和DALE的估计结果.计算实例表明了本文方法的有效性.

The estimation problem of matrix bounds for the continuous algebraic Lyapunov equation (CALE) and the discrete algebraic Lyapunov equation (DALE) could be considered by unified approach using delta operator. The upper and lower matrix bounds for the solution of the unified algebraic Lyapunov equation (UALE) are presented in terms of matrix inequality approach, and the obtained bounds reduce to existing ones for the continuous and discrete Lyapunov equations in the limiting cases. The proposed results are illustrated through an example.