Disturbance rejection with simultaneous linear exact model matching for a class of nonlinear systems

In this paper, the combined design problem of disturbance rejection and of linear exact model matching via static state or static state and measurement feedback is considered. A new approach is presented which solves the problem for a class of affine nonsquare nonlinear systems. The proposed approach reduces the problem of determining the feedback control law, with or without disturbance measurements, to that of solving a system of first-order partial differential equations. Based on this system of equations, algebraic (i.e. easily checkable) necessary and sufficient conditions for the design problem to have a solution are established. Furthermore, solving this system of equations, the general analytical expression for the feedback control law is explicitly determined.