On the minimal robust servo-regulator for nonlinear systems

It is shown in (Huang and Lin, 1991) that the kth-order robust nonlinear servomechanism problem can be solved by a class of linear controllers called kth-order robust servo-regulator. It is further shown in (Huang, 1995) that the kth-order robust servo-regulator, under one additional condition, also solves the (exact) robust nonlinear servomechanism problem. This paper further shows that the minimal dimension of this class of linear controllers is equal to the degree of the minimal polynomial of the k-fold exosystem multiplied by p, where p is the dimension of the regulated output. This result, coupled with a characterization of the minimal polynomial of the k-fold exosystem leads to a straightforward and efficient procedure to synthesize a minimal dimension linear robust servo-regulator.