TY - BOOK
T1 - Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems
AU - Heuvel, van den, P.J.
PY - 1980
Y1 - 1980
N2 - In this paper a generalization is proved of a theorem by Laroque (1979). This theorem asserts that if an autonomous system x = F(x) consists of linear subsystems defined on cones in R2 and if the function F(x) is continuous, then the origin is an asymptotically stable solution of the system, if the subsystems are asymptotically stable in R2. It is shown that the linearity restrictions in the theorem of Laroque can be relaxed in a neighbourhood of the equilibrium.
AB - In this paper a generalization is proved of a theorem by Laroque (1979). This theorem asserts that if an autonomous system x = F(x) consists of linear subsystems defined on cones in R2 and if the function F(x) is continuous, then the origin is an asymptotically stable solution of the system, if the subsystems are asymptotically stable in R2. It is shown that the linearity restrictions in the theorem of Laroque can be relaxed in a neighbourhood of the equilibrium.
M3 - Report
T3 - Memorandum COSOR
BT - Asymptotic stability of a solution of an autonomous system in R2, consisting of subsystems
PB - Technische Hogeschool Eindhoven
CY - Eindhoven
ER -