Y Shang Consensus in a class of nonlinear multi-agent systems with time-varying topologies (205K, Postscript) ABSTRACT. Most consensus protocols for multi-agent systems presented in the past do not consider nonlinear factors in the exchange of information between the agents. In this paper, we study a discrete-time nonlinear protocol for time-varying multi-agent systems described by stochastic matrices. Based on stochastic matrix theory, we provide convergence conditions (i.e., consensus criteria) for the systems subject to exponential decaying disturbances as well as general disturbances. Under the proposed framework, different convergence speeds, such as exponential convergence, can be achieved.