Performance bounds for disturbance attenuation in nonlinear non-minimum-phase systems

This paper addresses the problem of disturbance attenuation (in the sense of L
2
-Rain). with internal stability and no cost on the control input, for nonlinear system, when the problem of almost disturbance decoupling is not solvable, i.e. when the least achievable attenuation level between disturbance and regulated output is nonzero. Two different approaches are provided, which facilitate the estimation of an upper bound for such a value.