Journal
MATHEMATICAL MODELLING AND ANALYSIS
Volume 21, Issue 2, Pages 159-173Publisher
VILNIUS GEDIMINAS TECH UNIV
DOI: 10.3846/13926292.2016.1142481
Keywords
nonlinear multi-stage system; fundamental matrix solution; linear variational system; strong stability; 93C10; 37C75
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Funding
- National Natural Science Foundation of China [11171050, 11371164]
- National Science Foundation for the Youth of China [11301051, 11301081, 11501574]
- Provincial Natural Science Foundation of Fujian [2014J05001]
- Fundamental Research Funds for Central Universities in China [DUT15LK25]
- Natural Science Foundation of Shandong Province in China [ZR2015AL010]
- China Scholorship Council (CSC) [201506060121]
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In this paper, we consider a nonlinear multi-stage dynamic system to characterize batch culture. We construct corresponding linear variational system for the solution to the multi-stage system, also prove the boundedness of fundamental matrix solutions for the linear variational system. On this basis, we prove strong stability with respect to perturbance of initial state vector for the multi-stage system through the application of such boundedness. From extensive simulation study, it is observed that the strong stability is highly satisfactory.
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