TY - GEN
T1 - On the decidability of stability of hybrid systems
AU - Prabhakar, Pavithra
AU - Viswanathan, Mahesh
PY - 2012
Y1 - 2012
N2 - A rectangular switched hybrid system with polyhedral invariants and guards, is a hybrid automaton in which every continuous variable is constrained to have rectangular flows in each control mode, all invariants and guards are described by convex polyhedral sets, and the continuous variables are not reset during mode changes. We investigate the problem of checking if a given rectangular switched hybrid system is stable around the equilibrium point 0. We consider both Lyapunov stability and asymptotic stability. We show that checking (both Lyapunov and asymptotic) stability of planar rectangular switched hybrid systems is decidable, where by planar we mean hybrid systems with at most 2 continuous variables. We show that the stability problem is unde-cidable for systems in 5 dimensions, i.e., with 5 continuous variables.
AB - A rectangular switched hybrid system with polyhedral invariants and guards, is a hybrid automaton in which every continuous variable is constrained to have rectangular flows in each control mode, all invariants and guards are described by convex polyhedral sets, and the continuous variables are not reset during mode changes. We investigate the problem of checking if a given rectangular switched hybrid system is stable around the equilibrium point 0. We consider both Lyapunov stability and asymptotic stability. We show that checking (both Lyapunov and asymptotic) stability of planar rectangular switched hybrid systems is decidable, where by planar we mean hybrid systems with at most 2 continuous variables. We show that the stability problem is unde-cidable for systems in 5 dimensions, i.e., with 5 continuous variables.
KW - Decidability
KW - Stability
KW - Verification
UR - http://www.scopus.com/inward/record.url?scp=84876751241&partnerID=8YFLogxK
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U2 - 10.1145/2461328.2461339
DO - 10.1145/2461328.2461339
M3 - Conference contribution
AN - SCOPUS:84876751241
SN - 9781450315678
T3 - HSCC 2013 - Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control, Part of CPSWeek 2013
SP - 53
EP - 62
BT - HSCC 2013 - Proceedings of the 16th International Conference on Hybrid Systems
T2 - 16th International Conference on Hybrid Systems: Computation and Control, HSCC 2013 - Part of CPSWeek 2013
Y2 - 8 April 2013 through 11 April 2013
ER -