The paper studies input and state observability (ISO) of discrete-time linear time-invariant network systems whose dynamics are affected by unknown inputs. More precisely, we aim at reconstructing the initial state and the sequence of unknown inputs from the system outputs, and we will use the term ISO when the input reconstruction is possible with delay one, namely the inputs up to time $k-1$ and the states up to time $k$ can be obtained from the outputs up to time $k,$ while the term unconstrained ISO will refer to the case where there is some arbitrary delay in the input reconstruction. We focus on the problem of s-structural ISO (resp. s-structural unconstrained ISO) wherein the objective is to find conditions such that for all system matrices that carry the same network structure, the resulting system is ISO (resp. unconstrained ISO). We provide first a graphical characterization for s-structural unconstrained ISO, and subsequently, sufficient conditions and necessary conditions for s-structural ISO. For the latter, under the assumption of zero feedthrough, these conditions coincide and characterise ISO. The conditions presented are in terms of existence of suitable uniquely restricted matchings in bipartite graphs associated with the structured system. In order to test these conditions, we present polynomial-time algorithms. Finally, we discuss an equivalent reformulation of the main conditions in terms of coloring algorithms as in the literature of zero forcing sets.

本文研究了动态性受未知输入影响的离散时间线性时不变网络系统的输入和状态可观察性（ISO）。更准确地说，我们的目标是从系统输出中重建初始状态和未知输入的序列，当输入重建可能延迟一时（即直到时间的输入）时，我们将使用术语ISO。$ķ-\mathrm{1个}$ 和各州的时间 $ķ$ 可以从最新的输出中获得 $ķ，$“无约束ISO”一词是指输入重建中存在任意延迟的情况。我们专注于s结构ISO（即s结构非约束ISO）的问题，其目的是找到条件，使得对于带有相同网络结构的所有系统矩阵，最终系统为ISO（resp。unconstrained ISO） 。我们首先为s结构不受约束的ISO提供图形表征，然后为s结构ISO提供足够的条件和必要的条件。对于后者，在零馈通的假设下，这些条件一致并表征了ISO。呈现的条件是根据与结构化系统关联的二部图中存在适当的唯一受限匹配。为了测试这些条件，我们提出多项式时间算法。最后，我们讨论了与零强制集文献中的着色算法等效的主要条件重构。