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本文利用非负不可约矩阵的性质分析了灰色线性定常系统的稳定性问题,给出了灰色线性定常系统稳定性充分判据。所得判据不仅可用来分析灰色线性定常系统的稳定性,而且可用来分析线性时变系统的稳定性。作为所得判据的应用实例,本文还给出了确保线性时变系统稳定的充分条件。借此,可使很大一类线性时变系统的稳定性判定问题变得十分简单。
In this paper, the stability of gray linear systems is analyzed by using the properties of nonnegative irreducible matrices. The sufficient criteria for the stability of gray linear systems are given. The obtained criterion not only can be used to analyze the stability of gray linear system, but also can analyze the stability of linear time-varying system. As an applied example of the obtained criterion, the sufficient conditions for ensuring the stability of a linear time-varying system are also given. In this way, the problem of determining the stability of a very large class of linear time-varying systems becomes very simple.