广义区间动力系统稳定的充分条件

Sufficient Condition on the Stability of Descriptor Interval Systems

讨论了连续广义区间动力系统在系统矩阵为区间矩阵时的稳定性问题·根据Gershgorin圆盘定理,在假设广义区间动力系统满足系统矩阵A主对角线元素均为负区间数的约束条件下,给出了一个使广义区间动力系统正则、无脉冲膜且稳定的充分条件·针对系统对应的Gershgorin圆盘半径较大的情况做了进一步讨论,使上述充分条件能够适用于更一般的情况·举出实例说明了此方法的正确性,并给出了一个判别区间矩阵为非奇异的充分必要条件·

The stability for linear continuous time descriptor systems with an interval matrix was studied. Using Gershgorins theorem,a sufficient condition was derived to judge a descriptor interval system to be regular,impulse free and stable with the constraint that all the main diagonal values of the system matrix A are negative. Nevertheless, the sufficient condition was further developed to fit the case that the radius of the Gershgorin disc is comparatively large. Two examples were used to illustrate the validity of the method. And a necessary and sufficient condition is suggested to determine an interval matrix to be nonsingular.