TY - GEN
T1 - When is a set of LMIs a sufficient condition for stability
AU - Ahmadi, Amir Ali
AU - Jungers, Raphaël M.
AU - Parrilo, Pablo A.
AU - Roozbehani, Mardavij
PY - 2012/9/17
Y1 - 2012/9/17
N2 - We study stability criteria for discrete time switching systems and provide a meta-theorem that characterizes all the LMI-based Lyapunov theorems. For this purpose, we investigate the structure of sets of LMIs that are a sufficient condition for stability (i.e., such that any switching system which satisfies these LMIs is stable). Different such LMI conditions have been proposed in the last fifteen years, and we prove in this paper that a family of conditions recently provided by us actually encapsulates all the possible valid conditions. As a byproduct, we show that it is PSPACE-complete to recognize whether a particular set of LMIs implies the stability of a switching system.
AB - We study stability criteria for discrete time switching systems and provide a meta-theorem that characterizes all the LMI-based Lyapunov theorems. For this purpose, we investigate the structure of sets of LMIs that are a sufficient condition for stability (i.e., such that any switching system which satisfies these LMIs is stable). Different such LMI conditions have been proposed in the last fifteen years, and we prove in this paper that a family of conditions recently provided by us actually encapsulates all the possible valid conditions. As a byproduct, we show that it is PSPACE-complete to recognize whether a particular set of LMIs implies the stability of a switching system.
KW - Convex optimization
KW - Finite automata
KW - Hybrid systems
KW - Joint spectral radius
KW - Linear matrix inequalities
UR - http://www.scopus.com/inward/record.url?scp=84866111546&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84866111546&partnerID=8YFLogxK
U2 - 10.3182/20120620-3-DK-2025.00098
DO - 10.3182/20120620-3-DK-2025.00098
M3 - Conference contribution
AN - SCOPUS:84866111546
SN - 9783902823038
T3 - IFAC Proceedings Volumes (IFAC-PapersOnline)
SP - 313
EP - 318
BT - ROCOND'12 - 7th IFAC Symposium on Robust Control Design
T2 - 7th IFAC Symposium on Robust Control Design, ROCOND'12
Y2 - 20 June 2012 through 22 June 2012
ER -