# Dissipativity Analysis of Large-Scale Networked Systems
## 5 Conclusions  
This paper investigates the strict dissipativity of networked systems composed of a large number of subsystems. At first, according to the model of large-scale networked systems, the definition of the dissipativity of networked systems is given in this paper. Then, we study the dissipative criteria of networked systems. For large-scale networked systems, when the number of subsystems is large, the performance analysis using the existing linear system theory will encounter computational difficulties. Some LMI-form conditions for dissipativity analysis of large-scale networked systems are derived. Among them, Theorem 1 is a necessary and sufficient condition, which effectively utilizes the block diagonal structure of the system parameter matrix and the sparsity of the subsystem connection matrix. Combined with the use of sparse semidefinite programming tools, it is more efficient than the lumped analysis method for medium-scale networked systems. In addition, the proposed sufficient condition, and necessary condition only depend on the parameters of a single subsystem, which are more suitable for the dissipative analysis of networked systems with a large number of subsystems, but they are conservative compared with other conditions.  
Regarding large-scale networked systems, the design of distributed controllers to ensure the dissipativity of large-scale networked systems will be investigated in further research. For instance, in UAV formation flight, relying on a centralized controller to observe the entire formation and control all UAVs at once is both impractical and increases operational costs in engineering applications. A more reasonable option would be to decentralize the controller to each UAV platform and achieve the overall objective by interacting and sharing information between platforms. Therefore, if the structural information of the network topology is capable of being fully utilized and a distributed control strategy that relies on local information sharing is adopted, the amount of data transmission in the network will be greatly reduced and the computational efficiency will be raised. Furthermore, the presence of quantization errors, time delays, data packet loss, and other phenomena when communicating networked among subsystems or among subsystems and their local controllers will be explored. In practical engineering applications, network connections would possibly be non-idealized, and the arrival of information delivered is frequently unable to be achieved immediately.  
**Author Contributions:** Conceptualization, Y.S. and H.L.; methodology, Y.S.; software, Y.S.; validation, H.L.; formal analysis, Y.S.; investigation, Y.S.; resources, J.W. and H.L.; data curation, J.W.; writing--original draft preparation,Y.S.; writing--review and editing, Y.S.; visuConceptualizational, J.W. and H.L.; supervision, J.W. and H.L.; project administration, J.W. and H.L.; funding acquisition, J.W. and H.L. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work is supported by the National Natural Science Foundation of China under grant number 62273189; by the Shandong Provincial Natural Science Foundation under grant number ZR2019 MF063 and ZR2020 MF064.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.  
**Conflicts of Interest:** The authors declare no conflict of interest.