TY - GEN
T1 - Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions
AU - Peet, Matthew M.
AU - Papachristodoulou, Antonis
PY - 2008
Y1 - 2008
N2 - In this paper, we introduce the class of semi-separable kernel functions for use in constructing Lyapunov functions for distributed-parameter systems such as delaydifferential equations. We then consider the subset of semiseparable kernel functions defined by polynomials. We show that the set of such kernels which define positive forms can be parameterized by positive semidefinite matrices. In the particular case of linear time-delay systems, we show how to construct the derivative of Lyapunov functions defined by piecewise continuous semi-separable kernels and give numerical examples which illustrate some advantages over standard polynomial kernel functions.
AB - In this paper, we introduce the class of semi-separable kernel functions for use in constructing Lyapunov functions for distributed-parameter systems such as delaydifferential equations. We then consider the subset of semiseparable kernel functions defined by polynomials. We show that the set of such kernels which define positive forms can be parameterized by positive semidefinite matrices. In the particular case of linear time-delay systems, we show how to construct the derivative of Lyapunov functions defined by piecewise continuous semi-separable kernels and give numerical examples which illustrate some advantages over standard polynomial kernel functions.
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U2 - 10.1109/CDC.2008.4739245
DO - 10.1109/CDC.2008.4739245
M3 - Conference contribution
AN - SCOPUS:62949092984
SN - 9781424431243
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 847
EP - 852
BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 47th IEEE Conference on Decision and Control, CDC 2008
Y2 - 9 December 2008 through 11 December 2008
ER -