A Distributed Observer for a Class of Nonlinear Systems and Its Application to a Leader-Following Consensus Problem

In this note, we first present a framework for designing a distributed control law to solve a cooperative control problem of nonlinear multiagent systems with a nonlinear leader system. The distributed control law is composed of a purely decentralized control law and a distributed observer for the leader system, based on the certainty equivalence principle. Then, we establish a sufficient condition to guarantee the existence of a distributed observer for a class of nonlinear autonomous systems. The framework is then applied to solve the leader-following consensus problem for a class of high-order nonlinear heterogeneous multiagent systems subject to external disturbances. Our design is illustrated by an example with the Van der Pol system as the leader system.