一类分布参数混合系统的稳定性分析

Stability analysis of a class of distributed parameter hybrid systems

将混合系统推广到分布参数环境下,提出分布参数混合系统的概念.基于混合系统和分布参数系统的建模方法,建立了一类分布参数混合系统的模型,并对其稳定性进行分析.运用算子半群理论以及混合系统的五元组描述法及其稳定性关系比较理论的结论,通过选择适当的映射,将分布参数混合系统的的稳定性问题转化为集中参数下混合系统稳定性问题,进而得出了一致渐近稳定的充分条件并加以证明.仿真实例验证了文中结论的正确性.

A concept of distributed parameter hybrid systems （DPHS） is presented by introducing hybrid systems into distributed parameter systems. A model of a class of DPHS is given based on the modeling method of hybrid systems and distributed parameter systems. The stability of the class of DPHS is also studied. By using semigroup theory and the conclusions of stability comparison theory for quintuple of hybird system, the stability of a class of DPHS is transformed into the one of lumped parameter hybrid systems through an adequate mapping, and a sufficient condition of uniform and asymptotical stabilization of a class of DPHS is obtained and proved. Finally, a simulation example is given to demonstrate the correctness of the proposed conclusion.