This paper presents a novel Topological Distributed Multi-Rate State Estimator (TDMRSE) for designing a Distributed Output Feedback Exponential Sliding Mode Consensus (DOFESMC) protocol for a Discrete Multi-Agent System (DMAS) to achieve the leader-follower consensus. First, a topological distributed multi-rate state estimator is proposed for a DMAS using the graph theory where the stack of output at each agent is measured at a faster sampling rate than the input in DMAS. Then, the estimated state variables of each agent are used to design the DOFESMC protocol for DMAS to achieve the consensus by ensuring the minimal consensus effort, the minimum time for achieving the consensus, and the deviation of agents from the consensus of the order O(T^3). The condition for global consensus stability of DMAS with the proposed DOFESMC protocol is derived using the Lyapunov theory. The proposed DOFESMC protocol is validated in simulation and experiment on a DMAS comprised of 2-Degree of Freedom (DOF) robotic arms connected in a given communication topology. Moreover, the proposed protocol is compared with the protocol designed using a distributed Luenberger observer for consensus performance in terms of Integrated Square Error, control effort for consensus, and deviation from consensus. It is inferred from the simulation and experimental results that the proposed DOFESMC protocol with TDMRSE outperforms the protocol designed with a distributed Luenberger observer.