Most of contemporary storage rings operates in multibunch mode. In this case the transverse dynamics in the presence of feedback may be complicated. Indeed, in general case, the amplified signal of a beam position monitor kicks all circulating bunches. In this paper the stability of such system with many degrees of freedom is considered. Damping times are estimated for the simplest cases.
Results of researches supported by RBRF grant 15-02-07776 were used in this work.