arXiv:2610.28094v1 Announce Type: new Abstract: This paper addresses decentralized estimation and control of heterogeneous multi-agent systems communicating over directed switching topologies. The objective is to satisfy cooperative tasks that require coordination among agents according to a time-invariant task graph. To address the potential mismatch between the communication and task graphs, each agent is equipped with a k-hop Prescribed Performance State Observer (k-hop PPSO) to estimate the states of agents up to k communication hops away using only information exchanged with its 1-hop neighbors. A novel prescribed performance funnel construction is developed to account for the switching communication topology, and a sufficient lower bound on the dwell-time is derived to guarantee the prescribed performance specifications under topology variations. Further analysis shows that, if the desired control objective is achieved with exact knowledge of the required nonlocal states and the resulting closed-loop system is uniformly set-ISS with respect to the state estimation error, then replacing these states with their estimates guarantees convergence to a neighborhood of the desired set. The size of this neighborhood can be made arbitrarily small by appropriately selecting the observer performance bounds. A simulation study demonstrates task satisfaction under directed switching topologies.