TY - GEN
T1 - Towards robust Lie-algebraic stability conditions for switched linear systems
AU - Agrachev, Andrei A.
AU - Baryshnikov, Yuliy
AU - Liberzon, Daniel
N1 - Funding Information:
The work of Liberzon was supported by the NSF grant ECCS-0821153 and by the UIUC Center for Advanced Study .
PY - 2010
Y1 - 2010
N2 - This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. Two distinct approaches are investigated. For discrete-time switched linear systems, we formulate a stability condition in terms of an explicit upper bound on the norms of the Lie brackets. For continuous-time switched linear systems, we develop two stability criteria which capture proximity of the associated matrix Lie algebra to a solvable or a .solvable plus compact. Lie algebra, respectively.
AB - This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system parameters. Two distinct approaches are investigated. For discrete-time switched linear systems, we formulate a stability condition in terms of an explicit upper bound on the norms of the Lie brackets. For continuous-time switched linear systems, we develop two stability criteria which capture proximity of the associated matrix Lie algebra to a solvable or a .solvable plus compact. Lie algebra, respectively.
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U2 - 10.1109/CDC.2010.5717603
DO - 10.1109/CDC.2010.5717603
M3 - Conference contribution
AN - SCOPUS:79953141433
SN - 9781424477456
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 408
EP - 413
BT - 2010 49th IEEE Conference on Decision and Control, CDC 2010
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 49th IEEE Conference on Decision and Control, CDC 2010
Y2 - 15 December 2010 through 17 December 2010
ER -