A nonregular solution of the nonlinear dynamic disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem

The nonregular dynamic disturbance decoupling problem for nonlinear control systems is introduced. A local solution is given by means of a constructive algorithm that is based on Singh’s algorithm and the clamped dynamics algorithm. Further studied is the nonlinear model matching problem that is defined as follows: given a nonlinear control system, to be referred to as the plant, and another nonlinear control system, to be referred to as the model, can a compensator for the plant be found in such a way that the input-output behavior of the compensated plant matches that of the model? By proving that the solvability of the nonlinear model matching problem is equivalent to the solvability of an associated nonregular dynamic disturbance decoupling problem, a complete local solution of this problem can be established.