Distributed control of nonlinear uncertain systems: A cyclic-small-gain approach

This paper presents a cyclic-small-gain approach to distributed control of nonlinear multi-agent systems for output agreement. Through a novel nonlinear control law design, the output agreement problem is transformed into a stabilization problem, and the closed-loop multi-agent system is transformed into a large-scale system composed of input-to-state stability (ISS) subsystems which are interconnected with each other through redefined outputs. By forcing the redefined outputs to go to arbitrarily small neighborhoods of the origin, practical consensus is achieved for the agents in the sense that their outputs ultimately converge to each other within an arbitrarily small region. A recently developed cyclic-small-gain result is adopted to assign appropriately the ISS gains to the transformed interconnected system. Moreover, if the system is disturbance-free, then consensus can be guaranteed. Interestingly, the closed-loop multi-agent system is also robust to bounded time-delays and disturbances in information exchange.