TY - GEN
T1 - Positive forms and stability of linear time-delay systems
AU - Peet, Matthew
AU - Papachristodoulou, Antonis
AU - Lall, Sanjay
PY - 2006
Y1 - 2006
N2 - We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that stability implies that there exists a quadratic Lyapunov function on the state space, although this is in general infinite dimensional. We give an explicit parametrization of a finite-dimensional subset of the cone of Lyapunov functions. Positivity of this class of functions is enforced using sum-of-squares polynomial matrices. This allows the computation to be formulated as a semidefinite program.
AB - We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that stability implies that there exists a quadratic Lyapunov function on the state space, although this is in general infinite dimensional. We give an explicit parametrization of a finite-dimensional subset of the cone of Lyapunov functions. Positivity of this class of functions is enforced using sum-of-squares polynomial matrices. This allows the computation to be formulated as a semidefinite program.
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U2 - 10.1109/cdc.2006.376937
DO - 10.1109/cdc.2006.376937
M3 - Conference contribution
AN - SCOPUS:39549087963
SN - 1424401712
SN - 9781424401710
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 187
EP - 193
BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 45th IEEE Conference on Decision and Control 2006, CDC
Y2 - 13 December 2006 through 15 December 2006
ER -