Nonlinear regulation for linear fat plants: The constant reference/disturbance case

In this paper, the output regulation problem for linear time invariant systems is considered, for the case of fat plants and constant exogenous signals, including both references to be tracked and (measured or unmeasured) disturbances to be rejected. It is shown that nonlinear (in particular, piecewise linear solutions) of the regulator equations are optimal solutions when either (input or state) constraints or very reasonable performance indices are introduced; hence, such solutions might be preferable to the standard, well known and easy linear solutions.