Robust State Synchronization for High-Order Relative Degree Two MIMO Uncertain Nonlinear Multiagent Systems

We consider the problem of synchronizing the state of high order and relative degree two, nonlinear multiagent systems, in a leader-following scenario, with the leader dynamics being totally unknown to its followers. The agent dynamics has a full-entry and state-dependent control input matrix. In addition, all nonlinearities involved have unknown analytical expressions and, moreover, are affected by external additive disturbances. The proposed robust control protocol is distributed and of low analytical and computational complexity. When the underlying communication graph is directed, we prove that all disagreement errors converge to some arbitrarily small neighborhoods of zero in finite time, whose lower bound is user specified. Furthermore, all signals in the closed-loop remain bounded. In case the graph is undirected, the size of the aforementioned neighborhoods can be prescribed. The key ingredient of the proposed control scheme is an observer that estimates the second state of the leader with predefined accuracy and not later than a predetermined fixed time. To achieve the aforementioned attributes, each agent uses relative output information and its own state and transmits to its neighbors the estimation of the leader's second state derived by its observer. Simulations clarify and verify the theoretical findings.