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函数方法,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 function method is proposed for discrete time switched linear positive systems with dwell time, and a sufficient condition is established to ensure the asymptotic stability of the system in this paper. In addition, the method is used to analysis L1 gain of discrete time switched linear positive systems, a sufficient condition ensuring the unweighted γ–L1 gain of the system is derived. Further, a time-varying H∞ feedback control is designed for the system, which keeps the closed-loop system having a minimum γ–L1 gain. Finally, a numerical example is given to verify the conclusions.