X. Xu and P. J. Antsaklis
International Journal of Control, Vol.73, No.14, pp.1261-1279,
2000.
Abstract -- This paper studies and solves the problem of
asymptotic stabilization of switched systems consisting of
unstable second-order linear time-invariant (LTI) subsystems.
Necessary and sufficient conditions for asymptotic
stabilizability are first obtained. If a switched system is
asymptotically stabilizable, then the conic switching laws
proposed in the paper are used to construct a switching law that
asymptotically stabilizes the system. Switched systems consisting
of two subsystems with unstable foci are studied first and then
the results are extended to switched systems with unstable nodes
and saddle points. The results are applicable to switched systems
that consist of more than two subsystems.
[pdf file] [postcript
file]
Also released as Technical Report isis-99-001 [postcript file], [pdf file](Department of Electrical
Engineering, University of Notre Dame.