Acta Scientiarum Naturalium Universitatis Pekinensis

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Stability of A Class of Hybrid Dynamic Systems

YANG Peng,XIE Guangming,WANG Long   

  1. Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing, 100871
  • Received:2001-10-26 Online:2002-09-20 Published:2002-09-20



  1. 北京大学力学与工程科学系,系统与控制中心,北京,100871

Abstract: The stability condition of a class of hybrid dynamic systems is discussed. The characteristic of this class of hybrid dynamic systems is that a center controller controls N continuous plants in sharing time manner. The plants are described by differential equations. Event feedback strategy is used as the real-time scheduling policy such that only one plant is chosen to be controlled by the controller at any time. The main result of this paper is as follows: First, a discrete time system derived from the hybrid dynamic system with event feedback scheduling strategy is introduced, and it is shown that the stability of hybrid dynamic system is equivalent to that the state of the derived discrete time system tends to negative infinite. Based on this fact, a new proof of an existing stability condition is presented. Then, a conjecture as a new stability condition is proposed. It is showed that the conjecture holds in certain special cases. Finally, two numeric examples are presented to support the conjecture in general case.

Key words: hybrid dynamic systems, event feedback scheduling strategy, stability

摘要: 研究了一类混杂动态系统的稳定性条件。该类系统的特点是一个中央控制器以分时方式控制N个连续对象。每个对象均为线性定常系统,中央控制器以事件反馈调度策略选取某一对象进行控制。首先由混杂动态系统导出一个离散时间系统,指出混杂动态系统的稳定性等价于相应离散时间系统的状态趋向负无穷,基于此证明了一个系统稳定的充分性条件。其次,提出一个猜想作为新的充分性条件,并在一些特殊情况下证明猜想成立。最后给出两个数值例子作为一般情况下猜想的支持。

关键词: 混杂动态系统, 事件反馈调度策略, 稳定性

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