  When Model Predictive Control (MPC) is used in real-time to control linear
systems, quadratic programs (QPs) need to be solved within a limited time
frame. Recently, several parametric methods have been proposed that certify the
number of computations active-set QP solvers require to solve these QPs. These
certification methods, hence, ascertain that the optimization problem can be
solved within the limited time frame. A shortcoming in these methods is,
however, that they do not account for numerical errors that might occur
internally in the solvers, which ultimately might lead to optimistic complexity
bounds if, for example, the solvers are implemented in single precision. In
this paper we propose a general framework that can be incorporated in any of
these certification methods to account for such numerical errors.
