# A Review of Research on Diagnosability of Control Systems Based on Structural Analysis
## 1 Introduction  
With the continuing growth of industrial technology, the structural and functional complexity of control systems continuously grows [1]. The old tactics of enhancing the dependability of essential components and optimizing fault diagnosis algorithms are increasingly insufficient to fulfill the rising demand for fault diagnosis. On the one hand, increasing the reliability of the critical components not only increases the cost of the system design, production, and installation, it also cannot avoid the occurrence of faults [2]. On the other hand, the design of the fault diagnosis methods is limited by the fault information provided by the control system itself, which will inevitably affect the fault diagnosis performance if the fault information is insufficient or missing [3]. Therefore, enhancing the fault diagnosis performance from the source of the fault diagnosis is required to promote safety and reliability. Diagnosability is a design quality that describes the fault diagnosis performance, which may not only decide whether the fault can be detected but may also quantitatively describe the difficulty of the fault diagnosis [4]. Diagnosability is an important design feature to improve fault diagnosis performance. On the one hand, diagnosability ensures that the system's structure provides sufficient fault information. On the other hand, it also guarantees that the system can perform fault diagnosis work as cheaply and effectively as possible and that the control system maintains the fault diagnosis performance for its whole life cycle. [5]. Diagnosability, as an essential design feature of equipment, plays a vital role in the fields of electrical [6], railway [7], building [8], and manufacturing engineering [9], among others. By optimizing the design of the diagnosability structure and function of the system, the overall fault diagnosis performance and the fault tolerance of the system are improved. Structural analysis is a model-based fault diagnosis method [10]. It differs from the prior model-based fault diagnosis approaches that depended on the correct analytical model's design, analysis, and derivation. The structural analysis technique focuses on the structural model to acquire helpful information for fault detection and fault-tolerant control. The analytical model is converted into a structural model by analyzing the connection or structure between the unknown variables, known variables, and faults in the constraint equations (algebraic equations, differential equations, and difference equations), which are represented as bipartite diagrams or incidence matrices. Structural detectability and structural isolability are examined through structural decomposition [11]. Therefore, structural analysis is applied in the early design stage of the control system for fault diagnosability design [12]. First, the system is not yet finished. There is still ample design space; so, analyzing the system structure clarifies the structural detectability and isolability. Based on the diagnosability demand, a determination is made as to whether the system needs further modeling. Second, the diagnosability design based on structural analysis does not need to establish an accurate analytical model, which has the diagnosability design of some large and complex control systems. Third, structural analysis eliminates complex numerical operations, and the associated tools based on graph theory have superior efficiency compared to the analytical techniques. Fourth, owing to the disregard of the analytical formulation of the system constraint equations, the structural analysis provides significant benefits for the diagnosability research on nonlinear and differential algebraic system models. Establishing a structural model is a foundation for studying structural detectability and structural isolation and for designing residuals, sensor optimization, diagnosability optimization, and reconfigurability design [13].