A consensus problem has been studied in many fundamental and application fields to analyze coordinated behavior in multi-agent systems. In a consensus problem, it is usually assumed that a state of each agent is scalar and all agents have an identical linear consensus protocol. We present a consensus problem of multi-agent systems where each agent has multiple state variables and a performance value evaluated by a nonlinear performance function according to its current state. We derive sufficient conditions for agents to achieve consensus on the performance value using an algebraic graph theory and the mean value theorem. We also consider an application of a performance consensus problem to resource allocation in soft real-time systems so as to achieve a fair QoS (Quality of Service) level.

This paper addresses a discrete-time consensus problem with non-linear performance functions over dynamically changing communication topologies. Each agent has a performance value based on its internal information state and exchanges the performance value with other agents to achieve consensus. We derive sufficient conditions for a global consensus using algebraic graph theory.