切换正系统的渐近稳定性、L1增益及时变H∞控制
Asymptotic stability, L1 gain and time-varying H∞ control of switched positive systems

本文针对带有驻留时间约束的离散时间切换线性正系统, 提出了依赖驻留时间的时变分段线性余正Lyapunov 泛函方法, 得到确保系统渐近稳定的充分条件. 另外, 将此方法推广到离散切换正系统的L1 增益性分析中,得到系统具有未加权的γ-L1增益的充分条件. 进一步,对离散切换正系统设计一个时变H∞反馈控制, 使闭环系统具有最小γ-L1增益. 最后给出一个数值算例验证文中的结论.
A time-varying piecewise linear copositive Lyapunov functional method is proposed for discrete time switched linear positive systems with dwell time, and a sufficient condition is established to ensure the asymptotic sta- bility of the system. In addition, the method is used to analysis L1 gain of discrete time switched linear positive systems, a sufficient condition ensuring the unweighted γ-L1gain of the system is derived. Further, a time-varying H∞ feedbackcontrol is designed for the system, which keeps the closed-loop system having a minimum γ-L1gain. Finally, a numerical example is given to verify the conclusions