不确定参数闭环控制系统特征值的区间分析

运用区间理论，讨论了区间参数的结构振动控制问题，给出了求解闭环系统区间特征值的一种方法．基于区间参数导出了区间刚度矩阵和质量矩阵，然后利用矩阵摄动理论和区间扩张理论，推导了复区间特征值上下界估计的算法．这些结果是从二阶系统的左右特征向量出发得到的．将该文方法应用到悬臂梁的控制问题，数值结果表明它是有效的．

INTERVAL EIGENVALUES OF CLOSED-LOOP SYSTEMS OF UNCERTAIN STRUCTURES

Using the interval analysis, the vibration control problem of structures with interval parameters is discussed, which is approximated by a deterministic one. A method to solve the interval eigenalues of the closed-loop system is presented. Expressions of the interval stiffness and interval mass matrix are developed directly from the interval parameteers. With matrix perturbation and interval extension theory, an algorithm for estimating the upper and lower bounds of the interval complex eigenvalus is proposed. The results are derived in terms of eigenvalues and left and right eigenvectors of the second-order systems. The presented method is applied to a vibration system. The unmerical results show that the presented method is effective.