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Lyapunov stability of a class of discrete event systems

机译：一类离散事件系统的Lyapunov稳定性

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Discrete event systems (DES) are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals. "Logical" DES are a class of discrete time DES with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences. Recently, there has been much interest in studying the stability properties of logical DES and several definitions for stability, and methods for stability analysis have been proposed. Here the authors introduce a logical DES model and define stability in the sense of Lyapunov and asymptotic stability for logical DES. Then the authors show that more conventional analysis of stability which employs appropriate Lyapunov functions can be used for logical DES. The authors provide a general characterization of the stability properties of automata-theoretic DES models, Petri nets, and finite state systems. Furthermore, the Lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of N different types of parts according to a priority scheme (to prove properties related to the machine's ability to reorient itself to achieve safe operation) and a load balancing problem in computer networks (to study the ability of the system to achieve a balanced load to minimize underutilization).
机译：离散事件系统（DES）是动态系统，它通过在可能不规则的时间间隔发生事件而随时间变化。 “逻辑” DES是一类离散时间DES，其运动方程通常是非线性的，并且相对于事件发生是不连续的。近年来，人们对研究逻辑DES的稳定性和对稳定性的几种定义有极大的兴趣，并提出了用于稳定性分析的方法。在这里，作者介绍了逻辑DES模型并定义了Lyapunov意义上的稳定性和逻辑DES的渐近稳定性。然后，作者表明，采用适当Lyapunov函数的更常规的稳定性分析可以用于逻辑DES。作者提供了自动机理论DES模型，Petri网和有限状态系统的稳定性的一般表征。此外，在制造系统上演示了Lyapunov稳定性分析方法，该系统根据优先级方案（以证明与机器重新定向以实现安全操作的能力有关的属性）和负载平衡问题处理一批N种不同类型的零件。计算机网络（研究系统达到平衡负载以最大程度地减少未充分利用的能力）。

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