In this work we formulate the problem of satisfying a linear temporal logic formula on a linear plant with output feedback, through a recent hybrid systems formalism. We relate this problem to the notion of recurrence introduced for the considered formalism, and we then extend Lyapunov-like conditions for recurrence of an open, unbounded set. One of the proposed relaxed conditions allows certifying recurrence of a suitable set, and this guarantees that the high-level evolution of the plant satisfies the formula, without relying on discretizations of the plant. Simulations illustrate the proposed approach.

中文翻译：

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通过混合系统的递归工具满足线性时间逻辑规范

在这项工作中，我们通过最近的混合系统形式来制定在具有输出反馈的线性设备上满足线性时间逻辑公式的问题。我们将这个问题与为所考虑的形式主义引入的递归概念联系起来，然后我们扩展了类似李雅普诺夫的条件，用于开放无界集合的递归。提议的宽松条件之一允许证明合适集合的重复，这保证了植物的高级进化满足公式，而不依赖于植物的离散化。模拟说明了所提出的方法。