离散线性区间系统的分支稳定性

Componentwise Stability of Discrete Linear Interval Systems

研究了离散区间系统的一种特殊形式的稳定性 ,即分支稳定性。分别给出了离散区间系统分支渐近稳定性和指数分支渐近稳定性的定义。证明了离散区间系统是分支渐近稳定的 ,且仅当系统矩阵在每一时刻都将满足一个约束条件的系统状态向量变换成满足另一个约束的向量。

In this paper a special type of stability, namely componentwise stability for discrete linear interval systems is investigated. The componentwise asymptotic stability and componentwise asymptotic exponential stability of discrete interval systems are defined, respectively. It is shown that the systems are componentwise asymptotically stable if and only if the system matrices transform a vector in a constrained set into another constrained set each time. Lastly, based on property of inequalities, sufficient and necessary conditions for the componentwise asymptotic stability and componentwise asymptotic exponential stability of such systems are given respectively.