TY - GEN
T1 - Connections between stability conditions for slowly time-varying and switched linear systems
AU - Gao, Xiaobin
AU - Liberzon, Daniel
AU - Liu, Ji
AU - Basar, Tamer
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/8
Y1 - 2015/2/8
N2 - This paper establishes an explicit relationship between stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation of a matrix-valued function is introduced to characterize the variation of the system matrix. Using this concept, a result generalizing existing stability conditions for slowly time-varying linear systems is derived. As a special case of this result, it is shown that a switched linear system is globally exponentially stable if the average dwell time of the switching signal is large enough, which qualitatively matches known results in the literature.
AB - This paper establishes an explicit relationship between stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation of a matrix-valued function is introduced to characterize the variation of the system matrix. Using this concept, a result generalizing existing stability conditions for slowly time-varying linear systems is derived. As a special case of this result, it is shown that a switched linear system is globally exponentially stable if the average dwell time of the switching signal is large enough, which qualitatively matches known results in the literature.
UR - https://www.scopus.com/pages/publications/84962038073
U2 - 10.1109/CDC.2015.7402555
DO - 10.1109/CDC.2015.7402555
M3 - Conference contribution
AN - SCOPUS:84962038073
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 2329
EP - 2334
BT - 54rd IEEE Conference on Decision and Control,CDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th IEEE Conference on Decision and Control, CDC 2015
Y2 - 15 December 2015 through 18 December 2015
ER -