  This paper presents a framework for the study of convergence when the nodes'
dynamics may be both piecewise smooth and/or nonidentical across the network.
Specifically, we derive sufficient conditions for global convergence of all
node trajectories towards the same bounded region of their state space. The
analysis is based on the use of set-valued Lyapunov functions and bounds are
derived on the minimum coupling strength required to make all nodes in the
network converge towards each other. We also provide an estimate of the
asymptotic bound $\epsilon$ on the mismatch between the node states at steady
state. The analysis is performed both for linear and nonlinear coupling
protocols. The theoretical analysis is extensively illustrated and validated
via its application to a set of representative numerical examples.
