TY - GEN
T1 - SOS for nonlinear delayed models in biology and networking
AU - Papachristodoulou, Antonis
AU - Peet, Matthew M.
PY - 2009/10/19
Y1 - 2009/10/19
N2 - 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.
AB - 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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U2 - 10.1007/978-3-642-02897-7_12
DO - 10.1007/978-3-642-02897-7_12
M3 - Conference contribution
AN - SCOPUS:70349920934
SN - 9783642028960
T3 - Lecture Notes in Control and Information Sciences
SP - 133
EP - 143
BT - Topics in Time Delay Systems
A2 - Loiseau, Jean Jacques
A2 - Michiels, Wim
A2 - Niculescu, Silviu-Iulian
A2 - Sipahi, Rifat
ER -