TY - GEN
T1 - A methodology for determining the non-existence of common quadratic Lyapunov functions for pairs of stable systems
AU - Ordóñez-Hurtado, Rodrigo H.
AU - Duarte-Mermoud, Manuel A.
PY - 2011
Y1 - 2011
N2 - The existence of a common quadratic Lyapunov function (CQLF) for a switched linear system guarantees its global asymptotic stability. Although the progress in finding conditions for existence/non-existence of a CQLF has been significant in the last years, especially in switched linear systems with N subsystems of second order or two non-arbitrary subsystems of order n, the general case of N systems of order n still remains open. In this paper, based on a sufficient condition for the nonexistence of a CQLF for a pair of general subsystems of order n obtained from a lemma by Shorten et al., a new method for determining the non-existence of a CQLF, using Particle Swarm Optimization, is designed. A example illustrating the proposed method is introduced towards the end of the paper.
AB - The existence of a common quadratic Lyapunov function (CQLF) for a switched linear system guarantees its global asymptotic stability. Although the progress in finding conditions for existence/non-existence of a CQLF has been significant in the last years, especially in switched linear systems with N subsystems of second order or two non-arbitrary subsystems of order n, the general case of N systems of order n still remains open. In this paper, based on a sufficient condition for the nonexistence of a CQLF for a pair of general subsystems of order n obtained from a lemma by Shorten et al., a new method for determining the non-existence of a CQLF, using Particle Swarm Optimization, is designed. A example illustrating the proposed method is introduced towards the end of the paper.
KW - Common quadratic Lyapunov function
KW - Particle Swarm Optimization
KW - Stability of switched systems
UR - https://www.scopus.com/pages/publications/80455163114
U2 - 10.1109/ICGEC.2011.38
DO - 10.1109/ICGEC.2011.38
M3 - Conference contribution
AN - SCOPUS:80455163114
SN - 9780769544496
T3 - Proceedings - 2011 5th International Conference on Genetic and Evolutionary Computing, ICGEC 2011
SP - 127
EP - 130
BT - Proceedings - 2011 5th International Conference on Genetic and Evolutionary Computing, ICGEC 2011
T2 - 5th International Conference on Genetic and Evolutionary Computing, ICGEC2011
Y2 - 29 August 2011 through 1 September 2011
ER -