The gap between necessity and sufficiency for stability of sparse matrix systems: simulation studies

Sparse Matrix Systems

Yang, Tao

关键词: Sparse Matrix Systems;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/78554/YANG-THESIS-2015.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Sparse matrix systems (SMSs) are potentially very useful for graph analysis and topological representations of interaction and communication among elements within a system. Such systems’ stability can be determined by the Routh-Hurwitz criterion. However, simply using the Routh-Hurwitz criterion is not efficient in this kind of system. Therefore, a necessary condition can save a lot of work. The necessary condition is of importance and will be discussed in this thesis. Also, meeting the necessary condition does not mean it is safe to claim the SMS is stable. Therefore, another part of this project is to see how effective the necessary condition is by simulations. The simulation shows that approximate SMSs meeting the necessary condition are very likely to be stable. The results approach 90-95% effectiveness given enough trials.