混合系统的稳定性分析

研究了混合系统的稳定性问题.首先,对于混合系统给出了一种一般的模型,该模型能够描述混合状态的跳变现象.然后,定义了一种辅助函数作为系统能量的一种度量.基于该模型和辅助函数,得到了混合系统稳定性判定的一些新结果.这些结果给出了在离散状态改变时,在由于连续状态的跳变而引起的系统能量增加的情况下,混合系统仍保持稳定的充分条件.最后，给出了一种能量函数的寻找方案,并利用一个仿真实例验证了该方案的有效性.

STABILITY ANALYSIS OF HYBRID SYSTEMS

In this paper, the stability of hybrid systems is studied. At first, we give a general model for hybrid systems which can describe the jump phenomena of the hybrid states. Next, an auxiliary function is defined as the abstract measure of the system energy. Based on this model and the function, some new sufficient conditions for the stability of hybrid systems are established. Due to the jump of the hybrid states, the energy of the system may be increasing. In this case the stability of hybrid systems can be guaranteed by these new conditions. We then provide one method to search for the auxiliary function. At the end of the paper, the effectiveness of the method is illustrated by the simulation example.