Summary
In this chapter we illustrate how the Sum of Squares decomposition can be used for understanding the stability properties of models of models of biological and communication networks. The models we consider are in the form of nonlinear delay differential equations with multiple, incommensurate delays. Using the sum of squares approach, appropriate Lyapunov-Krasovskii functionals can be constructed, both for testing delay-independent and delay-dependent stability. We illustrate the methodology using examples from congestion control for the Internet and gene regulatory networks.
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Papachristodoulou, A., Peet, M.M. (2009). SOS for Nonlinear Delayed Models in Biology and Networking. In: Loiseau, J.J., Michiels, W., Niculescu, SI., Sipahi, R. (eds) Topics in Time Delay Systems. Lecture Notes in Control and Information Sciences, vol 388. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02897-7_12
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DOI: https://doi.org/10.1007/978-3-642-02897-7_12
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