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.

UR - http://www.scopus.com/inward/record.url?scp=62949092984&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62949092984&partnerID=8YFLogxK

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

T2 - 47th IEEE Conference on Decision and Control, CDC 2008

Y2 - 9 December 2008 through 11 December 2008

ER -