This paper investigates the observability and constructibility problems of time-varying linear dynamic equations using time scale theory. First, we define observability, reachability and constructibility operators on time scales. Some necessary and sufficient conditions are proposed to ensure the observability on non-uniform time domains based on some linear algebra tools. Then, constructibility is also examined using the same approach. Moreover, the link between observability and constructibility concepts on arbitrary time sets is discussed. Further, the observability and reachability duality relationship for time-varying linear systems on time scales is established. The current work unifies and extends some existing results given for standard cases (i.e. the continuous line and the discrete time domain) to non-uniform time domains. Finally, the obtained results are described with an illustrative example.

本文利用时间尺度理论研究了时变线性动力学方程的可观测性和可构造性问题。首先，我们在时间尺度上定义可观察性、可达性和可构造性算子。基于一些线性代数工具，提出了一些充分必要条件来保证非均匀时域的可观测性。然后，也使用相同的方法检查可构造性。此外，讨论了任意时间集上的可观察性和可构造性概念之间的联系。进一步建立了时变线性系统在时间尺度上的可观测性和可达性对偶关系。目前的工作将标准情况（即连续线和离散时域）给出的一些现有结果统一并扩展到非均匀时域。最后，