This paper considers the interval stability/stabilization as well as the $H_{\infty }$-performance constrained by convergence rate of the linear impulsive stochastic systems (LISSs). Firstly, based on the relationship between the system pole configuration and the system performance, a sufficient condition for the distribution of the system eigenvalues in a specific region is given, i.e., a new criterion for the interval stability/stabilization of LISSs. Meanwhile, a new algorithm is designed to precisely control the convergence speed of the target system by combining the interval stabilization method. In addition, an $H_{\infty }$ control criterion constrained by the convergence rate of the system is also proposed. Finally, the effectiveness and applicability of the method are verified by numerical examples.

本文考虑区间稳定性/稳定性以及$H_{\infty }$-性能受线性脉冲随机系统 (LISS) 的收敛速度限制。首先，基于系统极点配置与系统性能的关系，给出了系统特征值在特定区域内分布的充分条件，即LISSs区间稳定/稳定的新判据。同时，结合区间稳定方法，设计了一种新的算法来精确控制目标系统的收敛速度。此外，一个$H_{\infty }$还提出了受系统收敛速度约束的控制准则。最后通过数值算例验证了该方法的有效性和适用性。