This paper studies the stability and L₁-gain problems for impulsive positive switched systems (IPSS) consisting of both unstable and stable subsystems, and proposes a mode-dependent impulsive control (MDIC) method for the first time. By means of a piecewise linear co-positive Lyapunov function (PLCLF) and using average dwell time (ADT) approach, some sufficient criteria for global exponential stability (GES) and standard L₁-gain are established in terms of linear programming (LP), which can be verified conveniently by Matlab. A special impulsive controller is designed to guarantee the positivity and stability of the addressed system. Several numerical examples with simulations are provided to demonstrate the effectiveness of the obtained results.

本文研究了由不稳定子系统和稳定子系统组成的脉冲正切换系统（IPSS）的稳定性和L ₁增益问题，并首次提出了一种与模式有关的脉冲控制（MDIC）方法。通过分段线性共正Lyapunov函数（PLCLF）并使用平均停留时间（ADT）方法，根据线性规划（LP）建立了一些全局指数稳定性（GES）和标准L ₁增益的足够标准，可以通过Matlab方便地进行验证。设计了特殊的脉冲控制器，以确保所寻址系统的正性和稳定性。提供了几个带有模拟的数值示例，以证明所获得结果的有效性。