脉冲微分包含系统是具有状态脉冲的微分包含系统, 在建模层面有广泛的模型表征能力. 针对一类具有差分包含脉冲形式的线性脉冲微分包含系统, 文章探索系统在所有脉冲下的强稳定性, 给出基于Lyapunov 方法的稳定性判据. 特别地, 稳定性等价于存在一个联合公共范数, 使其对离散子动态诱导出具有压缩性质的公共矩阵范数, 及对连续子动态诱导出负值公共测度. 该判据可视为连续时间微分包含系统和离散时间差分包含系统相关稳定性判据的完全推广.

Impulsive differential inclusions are differential inclusions with impulse effects, which are capable of representing many real-world systems. For a class of impulsive differential inclusions with impulses of difference inclusions, we investigate the guaranteed stability under all impulses. A Lyapunov-like stability criterion is presented, which establishes the equivalence between the stability and the existence of a joint vector norm that induces negative common measure of the continuous sub-dynamics and contractive common matrix norm of the discrete sub-dynamics. The criterion is a complete extension of the well-known spectral abscissa/radius criteria for continuous-time/discrete-time differential/difference inclusions in the literature.