向量Lyapunov函数与集值微分系统的稳定性

摘要

The stability problem for a class of set-valued differential systems is investigated. By introducing the notion of upper quasi-monotone nondecreasing of functions, a new comparison principle, which connects the solutions to two higher-dimensional differential systems with the vector Lyapunov function, is presented. Meanwhile, using the comparison principle, some criteria on the qui-stability, equi-asymptotical stability and uniform equi-asymptoti-cal stability for the set-valued differential systems are obtained. Finally, an example was provided to illustrate the truth of the theorems.%讨论一类集值微分系统的稳定性问题.通过引入函数的上拟单调增的概念,并利用向量Lyapunov函数,给出连接两个高维系统解的新的比较定理.利用所得到的比较定理,给出集值微分系统等度稳定,等度渐近稳定和一致等度渐近稳定的判别准则.实例分析验证了所得结果的正确性.