Title :
Networks of passive oscillators
Author :
Kulkarni, Vishwesh V. ; Riedel, Marc ; Stan, Guy-Bart
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Minneapolis, MN, USA
Abstract :
We present new results on the synthesis of globally stable limit cycles in networks of passive oscillators. These passive oscillators can be represented as a modified multi- input-multi-output (MIMO) Lure´ system that is dissipative with respect to a certain supply rate. We use KS multipliers to establish the conditions under which the system undergoes either Hopf bifurcation or a pitchfork bifurcation. Under these conditions the network exhibits oscillations. Our results are applicable to networks of non-identical oscillators so long as the each oscillator is a passive oscillator.
Keywords :
bifurcation; biomedical electronics; oscillators; Hopf bifurcation; KS multipliers; MIMO Lure system; multiple-input multiple-output Lure system; passive oscillators; pitchfork bifurcation; Asymptotic stability; Bifurcation; Limit-cycles; MIMO; Manifolds; Oscillators; Stability analysis; Hopf bifurcation; KS multipliers; Lure´ systems; Zames-Falb multipliers; global stability; oscillators; pitchfork bifurcation;
Conference_Titel :
Communication, Control, and Computing (Allerton), 2011 49th Annual Allerton Conference on
Conference_Location :
Monticello, IL
Print_ISBN :
978-1-4577-1817-5
DOI :
10.1109/Allerton.2011.6120216
