Adding resets to an average consensus algorithm to achieve practical input-to-output stability

We consider the average consensus problem when the data points to be averaged are contained in a known compact set. We add resets to an existing dynamic average consensus algorithm to achieve practical input-to-output stability (IOS) from a variety of disturbances to the mismatch between the true average and the computed average. The disturbances considered include communication errors, numerical round-off errors, and time-varying errors added to the data being averaged. The practical IOS result is a corollary of an input-to-state stability (ISS) result; the latter is established using recently-developed results for hybrid dynamical systems, including conditions for global asymptotic stability of an Omega-limit set, a converse Lyapunov theorem, and a Lyapunov-based sufficient condition for input-to-state stability.