Abstract This work investigates the observability analysis and the observer synthesis for Linear Hybrid Systems ( L H S ’s) considering both known and unknown inputs and constrained discrete dynamics. In this framework, none assumption is made over the unknown inputs (that can represent faults or disturbances), moreover, the discrete dynamics are represented by a Petri net, whose behaviour constraints the possible switchings. For this, the concept of eventual observability is considered as the possibility of uniquely determining both the discrete and the continuous states after a finite number of switchings. In this way, the information provided by the continuous and the discrete outputs of the L H S is combined to determine the discrete state after a finite number of switchings. Next, based on the knowledge of the visited discrete states, a continuous observer estimates the continuous state. Under this approach, neither the observability of the linear systems nor the observability of the underlying discrete event system are required for estimating the complete state of the L H S .

中文翻译：

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具有未知输入和 Petri-net 离散动力学的线性混合系统的观察者设计

摘要 这项工作研究了线性混合系统 (LHS) 的可观测性分析和观测器综合，同时考虑了已知和未知输入以及受约束的离散动力学。在这个框架中，对未知输入（可以代表故障或干扰）不做任何假设，而且离散动态由 Petri 网表示，其行为限制了可能的切换。为此，最终可观察性的概念被认为是在有限次数的切换后唯一确定离散和连续状态的可能性。这样，将 LHS 的连续输出和离散输出提供的信息结合起来，确定有限次开关后的离散状态。接下来，基于所访问的离散状态的知识，连续观察者估计连续状态。在这种方法下，估计 LHS 的完整状态既不需要线性系统的可观测性，也不需要底层离散事件系统的可观测性。