TY - GEN
T1 - Common Lyapunov function computation for discrete-time systems
AU - Hafstein, Sigurdur Freyr
N1 - Publisher Copyright: © 2018 IEEE.
PY - 2019/1/18
Y1 - 2019/1/18
N2 - We describe an algorithm to compute a common Lyapunov function for a finite set of nonlinear discrete-time systems. In this algorithm a compact neighbourhood of a common equilibrium of the systems is subdivided into simplices and a linear programming problem is constructed. We prove that any feasible solution to this linear programming problem can be used to parameterize a common Lyapunov function for the systems that is continuous and affine on each of the simplices of the triangulation. We conclude the paper by applying our algorithm to two planar examples.
AB - We describe an algorithm to compute a common Lyapunov function for a finite set of nonlinear discrete-time systems. In this algorithm a compact neighbourhood of a common equilibrium of the systems is subdivided into simplices and a linear programming problem is constructed. We prove that any feasible solution to this linear programming problem can be used to parameterize a common Lyapunov function for the systems that is continuous and affine on each of the simplices of the triangulation. We conclude the paper by applying our algorithm to two planar examples.
UR - https://www.scopus.com/pages/publications/85062192366
U2 - 10.1109/CDC.2018.8619234
DO - 10.1109/CDC.2018.8619234
M3 - Conference contribution
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3211
EP - 3216
BT - 2018 IEEE Conference on Decision and Control, CDC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 57th IEEE Conference on Decision and Control, CDC 2018
Y2 - 17 December 2018 through 19 December 2018
ER -