  We study cooperative control dynamics with gradient based forcing terms. As a
specific example, we focus on source-seeking dynamics with vehicles embedded in
an unknown scalar field with a subset of agents having gradient information. As
interaction mechanisms, formation control dynamics and flocking dynamics are
considered. We leverage the framework of $\alpha$-integral quadratic
constraints to obtain convergence rate estimates whenever exponential stability
can be achieved. The communication graph and the interaction potential are
assumed to be time-invariant and uncertain. Sufficient conditions take the form
of linear matrix inequalities independent of the size of network. A derivation
(purely in time-domain) of the so-called \textit{hard} Zames-Falb $\alpha$-IQCs
involving general non-causal higher order multipliers is given along with a
suitably adapted parameterization of the multipliers to the $\alpha$-IQC
setting. The time-domain arguments facilitate a straightforward extension to
linear parameter varying systems. Numerical examples illustrate the application
of the theoretical results.
