According to the
multiple Lyapunov function method, the switching system is stable [6]. The node
will converge to the ?± region. In the region ?±, the node then converges to equilibrium
E?????? for the situation shown in Figure 5 (a). The convergence analysis for the situation
shown in Figure 5 (b) is similar, the node will converge to equilibrium E??? in this case.
(a) (b)
Fig. 7. Convergence analysis with topological events.
Figure 7 shows two different situations where the equilibria belong to different
regions of ? or ???
, or one of the equilibria is on the co-circle. The analysis for the
convergence to the ?± region is the same. However, after the node enters region ?±,
then it is bi-stable for the situation shown in Figure 7 (a). This is concluded by the
fact that the difference of topology structure A??? and A?????? is link AC, which adds to
additional potential energy to VA?????? . If a topological event occurs inside of region ?±,
the increment of VA??? leads to the decrement of VA?????? and vice versa, which may cause
resonance. The potential field VA?????? is a linear addition of VA??? and the potential energy
generated by link AC. However, the increment generated by link AC is bounded,
thus the topological event can only occur finite times; the node will enter a small
region around E??? or E?????? and then converge. Depending on the initial position in
region ?±, it may converge to either equilibria.
Pages:
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147