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研究了一般的非线性系统生存性问题.首先由基于微分包含的生存理论,给出了非线性系统在不等式表示区域上生存的充要条件,然后证明了非线性系统在平衡点的李亚普诺夫稳定性等价于系统在其任意李亚普诺夫函数水平集上的生存性,从而确定了李亚普诺夫函数水平集即为系统的生存域.另外,基于无源性理论还证明了通过适当的输出反馈,可以使得系统在由存储函数确定的区域上是生存的,从而得到系统的生存域.最后仿真结果验证了所得结论的正确性.
In this paper, we study the general existence of non-linear system’s survivability problem.Firstly, based on the existence theory of differential inclusion, we give the necessary and sufficient conditions for the existence of nonlinear system in the inequality representation area, and then prove that Lyapunov The stability is equivalent to the survivability of the system on any Lyapunov function level set, so that the Lyapunov function level set is determined as the survival of the system.In addition, based on the passive theory, The feedback can make the system survive in the area determined by the storage function and get the survival domain of the system.Finally, the simulation results verify the correctness of the conclusion.