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Yang, Tao 2015-07-22T22:18:11Z 2015-07-22T22:18:11Z 2015-05 2015-04-30 2015-5 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-07-22 without embargo terms The student, Tao Yang, accepted the attached license on 2015-04-29 at 18:04. The student, Tao Yang, submitted this Thesis for approval on 2015-04-29 at 18:13. This Thesis was approved for publication on 2015-04-30 at 10:13. DSpace SAF Submission Ingestion Package generated from Vireo submission #8200 on 2015-07-22 at 10:34:58 Made available in DSpace on 2015-07-22T22:18:11Z (GMT). No. of bitstreams: 2 YANG-THESIS-2015.pdf: 848019 bytes, checksum: 617755de1b2243af9935c6af7bc37b88 (MD5) LICENSE.txt: 4205 bytes, checksum: 039528ac42c9d0537d69f3f76afb246a (MD5) Previous issue date: 2015-04-30 application/pdf http://hdl.handle.net/2142/78554 en Copyright 2015 Tao Yang Sparse Matrix Systems The gap between necessity and sufficiency for stability of sparse matrix systems: simulation studies text text Electrical & Computer Eng Electrical & Computer Engr University of Illinois at Urbana-Champaign Thesis M.S.