  Guaranteed-cost consensus for high-order nonlinear multi-agent networks with
switching topologies is investigated. By constructing a time-varying
nonsingular matrix with a specific structure, the whole dynamics of multi-agent
networks is decomposed into the consensus and disagreement parts with nonlinear
terms, which is the key challenge to be dealt with. An explicit expression of
the consensus dynamics, which contains the nonlinear term, is given and its
initial state is determined. Furthermore, by the structure property of the
time-varying nonsingular transformation matrix and the Lipschitz condition, the
impacts of the nonlinear term on the disagreement dynamics are linearized and
the gain matrix of the consensus protocol is determined on the basis of the
Riccati equation. Moreover, an approach to minimize the guaranteed cost is
given in terms of linear matrix inequalities. Finally, the numerical simulation
is shown to demonstrate the effectiveness of theoretical results.
