切换非线性正系统的有限时间稳定性

研究模型依赖平均驻留时间(MDADT)切换信号下一类齐次度为1的切换非线性正系统的有限时间稳定问题.首先,通过构造恰当的切换最大分离Lyapunov函数,借助于Dini导数,基于MDADT切换信号,给出切换非线性正系统有限时间稳定的充分条件.与已有的指数稳定性结果相比,进一步说明有限时间稳定与指数稳定的区别.其次,将所得结论应用于切换线性正系统,得到切换线性正系统在MDADT或平均驻留时间(ADT)切换信号下有限时间稳定的充分条件.最后,通过仿真算例验证所得结论的有效性.

Finite-time stability of switched nonlinear positive systems

In this paper, the finite-time stability for a class of switched nonlinear positive systems of degree one is investigated under the mode-dependent average dwell time(MDADT) switching signal. Firstly, by constructing an appropriate switched max-type separate Lyapunov function, based on the MDADT switching signal, a sufficient condition for the finite-time stability of the switched nonlinear positive systems is given with the aid of Dini derivative. Comparision with the existing results of exponential stability, it further illustrates the difference between finite-time stability and exponential stability. Secondly, the result is applied to the switched linear positive systems, and some sufficient conditions for the finite-time stability of the switched linear positive systems under MDADT or average dwell time(ADT) switching signals are obtained. Finally, the simulation examples are given to illustrate the effectiveness of the conclusion.