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This work is concerned with the problem of output consensus for two classes of heterogeneous nonlinear multiagent systems which are interconnected via diffusive couplings over directed graphs. Specifically, for agents that are input feedforward passive (IFP), a condition in terms of passivity indices is proposed for asymptotic output consensus. Moreover, it is shown that the proposed condition can be exploited to design the coupling gain that ensures asymptotic consensus via a semidefinite program (SDP), and the existence of such a coupling gain can be guaranteed provided all the agents are IFP. For agents that are input feedforward output feedback passive (IF-OFP), a condition in terms of passivity indices for practical output consensus is provided, in which the relationship between the coupling gain and the consensus error bound is revealed.

In this work, we address the distributed optimization problem with event-triggered communication by introducing the notion of input feedforward passivity (IFP). First, we analyze a distributed continuous-time algorithm over uniformly jointly strongly connected balanced digraphs and show its exponential convergence over strongly connected digraphs. Then, we propose an event-triggered communication mechanism for this algorithm. Next, we discretize the continuous-time algorithm by the forward Euler method and show that the discretization can be seen as a stepsize dependent passivity degradation of the input feedforward passivity. The discretized system preserves IFP property and enables the same event-triggered communication mechanism but without Zeno behavior due to its sampling nature. Finally, a numerical example is presented to illustrate our results.