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.

UR - http://www.scopus.com/inward/record.url?scp=39549087963&partnerID=8YFLogxK

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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 -