Decoupling in nonlinear systems: from linearity to nonlinearity

A standard approach for dealing with synthesis problems in nonlinear control systems consists in linearising the nonlinear system around a specific working point and, then, solving the synthesis problem for the obtained linear system. To what extent the resulting linear controller is a good approximate solution for the nonlinear problem is questionable. The authors discuss, as an example, the input/output decoupling problem. It is shown that, under fairly general conditions, the solvability requirements for the nonlinear and the corresponding linear problem are the same. The authors also characterise those linear solutions which are first-order solutions for the nonlinear problem. Simulations on a few fairly simple examples illustrate the results obtained.