Abstract: For switched positive linear systems, the exponential stability analysis of switching signals with pre-given dwell time is discussed by using the time-varying linear co-positive Lyapunov function method. Firstly, by constructing the time-varying linear co-positive Lyapunov functions, sufficient conditions on the global exponential stability of the switched positive linear system are obtained under the dwell time switching signal with the upper and lower bound constraints. Secondly, sufficient conditions on the global exponential stability of switched positive linear system are also given by specifying the lower bound of the dwell time. All conditions can be written in the form of linear programming problems. Finally, an example is given to show the effectiveness of the proposed method. 

Key words: Switched positive linear system, stability analysis, time-varying co-positive Lyapunov function, dwell time

摘要： 针对切换正线性系统，利用时变余正Lyapunov函数方法，讨论其在预先给定驻留时间切换信号下的指数稳定性分析问题。首先，当驻留时间满足上下界约束时，通过构造时变余正Lyapunov函数，建立了切换正线性系统指数稳定的充分条件。其次，研究了驻留时间切换信号在仅有下界约束情形下，切换正线性系统全局指数稳定的充分条件。所提出的条件均可以用线性规划算法来求解。最后，通过数值例子验证所提方法的有效性。

关键词: 切换正线性系统, 指数稳定性, 时变余正Lyapunov函数, 驻留时间