基于稳定性和无源性的非线性系统生存性分析  

Viability Analysis for Nonlinear System Based on Stability and Passivity

作　　者：娄志娥[1,2] 董潇潇[3] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110819 [2]蚌埠学院理学系,安徽蚌埠233030 [3]沈阳工业大学理学院,辽宁沈阳110001

出　　处：《信息与控制》2015年第1期125-128,共4页Information and Control

基　　金：安徽省自然科学基金资助项目(1408085QA10);辽宁省教育厅科学研究一般资助项目(L2013047);安徽省教育厅自然科学研究一般项目(KJ2012B099)

摘　　要：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.The viability problem for general nonlinear systems is investigated. First, the necessary and sufficient conditions for determining the viability of the nonlinear system on a region expressed by an inequality are de- veloped using the viability theory based on differential inclusions. Next, it is proved that the Lyapunov stabili- ty for the nonlinear system on the equilibrium is equivalent to the viability of the system on arbitrary Lyapunov function level sets, and it is determined that the Lyapunov function level set is the viable domain. In addi- tion, on the basis of passivity, it is also proved that through the appropriate output feedback, the system can be made viable on the region determined by the storage function, and at the same time, the viable domain is acquired. Finally, the simulation results show the correctness of the conclusions.

关 键 词：微分包含 生存性 稳定性 无源性 生存域 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]