  We analyze the performance of source-seeking dynamics involving either a
single vehicle or multiple flocking-vehicles embedded in an underlying strongly
convex scalar field with gradient based forcing terms. For multiple vehicles
under flocking dynamics embedded in quadratic fields, we show that the dynamics
of the center of mass are equivalent to the dynamics of a single agent. We
leverage the recently developed framework of $\alpha$-integral quadratic
constraints (IQCs) to obtain convergence rate estimates. We first present a
derivation of \textit{hard} Zames-Falb (ZF) $\alpha$-IQCs involving general
non-causal multipliers based on purely time-domain arguments and show that a
parameterization of the ZF multiplier, suggested in the literature for the
standard version of the ZF IQCs, can be adapted to the $\alpha$-IQCs setting to
obtain quasi-convex programs for estimating convergence rates. Owing to the
time-domain arguments, we can seamlessly extend these results to linear
parameter varying (LPV) vehicles possibly opening the doors to non-linear
vehicle models with quasi-LPV representations. We illustrate the theoretical
results on a linear time invariant (LTI) model of a quadrotor, a non-minimum
phase LTI plant and two LPV examples which show a clear benefit of using
general non-causal dynamic multipliers to drastically reduce conservatism.
