Switching max-plus linear system (SMPLS) models are an apt formalism for performance analysis of discrete-event systems. SMPLS analysis is more scalable than analysis through other formalisms such as timed automata, because SMPLS abstract pieces of determinate concurrent system behavior into atomic modes with fixed timing. We consider discrete-event systems that are decomposed into a plant and a Supervisory Controller (SC) that controls the plant. The SC needs to react to events, concerning e.g. the successful completion or failure of an action, to determine the future behavior of the system, for example, to initiate a retrial of the action. To specify and analyze such system behavior and the impact of feedback on timing properties, we introduce an extension to SMPLS with discrete-event feedback. In this extension, we model the plant behavior with system modes and capture the timing of discrete-event feedback emission from plant to SC in the mode matrices. Furthermore, we use I/O automata to capture how the SC responds to discrete-event feedback with corresponding mode sequences of the SMPLS. We define the semantics of SMPLS with events using new state-space equations that are akin to classical SMPLS with dynamic state-vector sizes. To analyze the extended models, we formulate a transformation from SMPLS with events to classical SMPLS with equivalent semantics and properties such that performance properties can be analyzed using existing techniques. Our approach enables the specification of discrete-event feedback from the plant to the SC and its performance analysis. We demonstrate our approach by specifying and analyzing the makespan of a flexible manufacturing system.

切换最大加线性系统 (SMPLS) 模型是离散事件系统性能分析的一种合适的形式。SMPLS 分析比通过其他形式（例如定时自动机）进行的分析更具可扩展性，因为 SMPLS 将确定的并发系统行为抽象为具有固定定时的原子模式。我们考虑将离散事件系统分解为一个工厂和一个控制该工厂的监控控制器 (SC)。SC 需要对事件做出反应，例如涉及操作的成功完成或失败，以确定系统的未来行为，例如启动操作的重试。为了指定和分析此类系统行为以及反馈对时序属性的影响，我们引入了具有离散事件反馈的 SMPLS 扩展。在这个扩展中，我们用系统模式对植物行为进行建模，并在模式矩阵中捕获从植物到 SC 的离散事件反馈发射的时间。此外，我们使用 I/O 自动机来捕获 SC 如何响应离散事件反馈以及 SMPLS 的相应模式序列。我们使用新的状态空间方程定义带有事件的 SMPLS 语义，该方程类似于具有动态状态向量大小的经典 SMPLS。为了分析扩展模型，我们制定了从具有事件的 SMPLS 到具有等效语义和属性的经典 SMPLS 的转换，以便可以使用现有技术来分析性能属性。我们的方法可以指定从工厂到 SC 的离散事件反馈及其性能分析。