Caputo分数阶切换线性系统的指数稳定性

Exponential stability of Caputo fractional order switched linear system

众所周知,与整数阶切换系统不同, Caputo分数阶切换系统的积分下界不能随子系统的切换而被更新,意味着在下界非一致的任意区间内不能直接取分数阶导数的分数阶积分.对此,本文给出了一个不等式(文中引理6)克服这一问题,并用1个数值例子进行了验证.通过这一不等式,然后分别利用多Lyapunov函数方法和模型依赖平均驻留时间(MDADT)方法,给出了Caputo分数阶切换线性系统指数稳定的条件,并利用2个数值例子进行验证.

As we all know,different from the integer order switched systems,the integral lower bound of Caputo fractional order switched systems cannot be updated with the switching of subsystems,which means that the fractional integral of fractional derivative cannot be taken directly in any interval with non-uniform lower bound.In order to overcome the above problem,an inequality(Lemma 6)is given in this paper.Through this inequality,the sufficient condition for the exponential stability of Caputo fractional order switched linear systems is given by using the multiple Lyapunov function and the model-dependent average dwell time(MDADT)method,respectively.Finally,two number examples are provided to verify the results.