TY - GEN
T1 - LMI parametrization of Lyapunov functions for infinite-dimensional systems
T2 - 2014 American Control Conference, ACC 2014
AU - Peet, Matthew
PY - 2014
Y1 - 2014
N2 - In this paper, we present an algorithmic approach to the construction of Lyapunov functions for infinite-dimensional systems. This paper unifies and significantly extends many previous results which have appeared in conference and journal format. The unifying principle is that any linear parametrization of operators in Hilbert space can be used to construct an LMI parametrization of positive operators via squared representations. For linear systems, we get positive linear operators and hence quadratic Lyapunov functions. For nonlinear systems, we get nonlinear operators and hence non-quadratic Lyapunov functions. Special cases of these results include positive operators defined by multipliers and kernels which are: polynomial; piecewise-polynomial; or semi-separable and apply to systems with delay; multiple spatial domains; or mixed boundary conditions. We also introduce a set of efficient software tools for creating these functionals. Finally, we illustrate the approach with numerical examples.
AB - In this paper, we present an algorithmic approach to the construction of Lyapunov functions for infinite-dimensional systems. This paper unifies and significantly extends many previous results which have appeared in conference and journal format. The unifying principle is that any linear parametrization of operators in Hilbert space can be used to construct an LMI parametrization of positive operators via squared representations. For linear systems, we get positive linear operators and hence quadratic Lyapunov functions. For nonlinear systems, we get nonlinear operators and hence non-quadratic Lyapunov functions. Special cases of these results include positive operators defined by multipliers and kernels which are: polynomial; piecewise-polynomial; or semi-separable and apply to systems with delay; multiple spatial domains; or mixed boundary conditions. We also introduce a set of efficient software tools for creating these functionals. Finally, we illustrate the approach with numerical examples.
KW - Delay systems
KW - Distributed parameter systems
KW - LMIs
UR - http://www.scopus.com/inward/record.url?scp=84905715632&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84905715632&partnerID=8YFLogxK
U2 - 10.1109/ACC.2014.6859228
DO - 10.1109/ACC.2014.6859228
M3 - Conference contribution
AN - SCOPUS:84905715632
SN - 9781479932726
T3 - Proceedings of the American Control Conference
SP - 359
EP - 366
BT - 2014 American Control Conference, ACC 2014
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 4 June 2014 through 6 June 2014
ER -