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

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.