This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential inclusions -- capturing the continuous dynamics -- and difference inclusions -- capturing the discrete dynamics or events -- with constraints. State trajectories (or solutions) to such systems are parameterized by a hybrid notion of time. For such broad class of solutions, the operators and semantics needed to reason about temporal logic are introduced. Characterizations of temporal logic formulas in terms of dynamical properties of hybrid systems are presented -- in particular, forward invariance and finite time attractivity. These characterizations are exploited to formulate sufficient conditions assuring the satisfaction of temporal logic formulas -- when possible, these conditions do not involve solution information. Combining the results for formulas with a single operator, ways to certify more complex formulas are pointed out, in particular, via a decomposition using a finite state automaton. Academic examples illustrate the results throughout the paper.

中文翻译：

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混合动力系统的线性时序逻辑：特征和充分条件

本文介绍了运算符、语义、特征和独立于解决方案的条件，以保证混合动力系统的时间逻辑规范。混合动力系统根据差分包含（捕获连续动态）和差异包含（捕获离散动态或事件）和约束条件给出。此类系统的状态轨迹（或解决方案）由混合时间概念参数化。对于如此广泛的解决方案，引入了推理时间逻辑所需的运算符和语义。根据混合系统的动态特性，提出了时序逻辑公式的特征——特别是前向不变性和有限时间吸引力。利用这些特征来制定充分条件，确保满足时序逻辑公式——如果可能，这些条件不涉及解信息。将公式的结果与单个运算符相结合，指出了证明更复杂公式的方法，特别是通过使用有限状态自动机的分解。学术实例说明了整篇论文的结果。