In this paper, the contraction theory is used to solve the robust
trajectory tracking control method for distributed complex nonlinear
systems. The controller designed by the contraction theory can make the
system track any trajectory and get rid of the assumption of the stable
point of the Lyapunov method. For complex nonlinear systems, parts with
unknown parameters or difficult to model will have a great impact on
controller design. Neural network is used to compensate the
uncertainties of the model, and a global linear matrix inequality (LMI)
which satisfies distributed robust trajectory tracking is proposed. A
decomposition method of global linear matrix inequalities (LMIS) is
presented to meet the solving requirements of distributed controllers.
The rationality of the matrix inequality proposed in this paper is
verified by theoretical analysis.