  Motivated by increasing precision requirements for switched power amplifiers,
this paper addresses the problem of model predictive control (MPC) design for
discrete-time linear systems with a finite control set (FCS). Typically,
existing solutions for FCS-MPC penalize the output tracking error and the
control input rate of change, which can lead to arbitrary switching among the
available discrete control inputs and unpredictable steady-state behavior. To
improve the steady-state behavior of FCS-MPC, in this paper we design a cost
function that penalizes the tracking error with respect to a state and input
steady-state limit cycle. We prove that if a suitable terminal cost is added to
the FCS-MPC algorithm convergence to the limit cycle is ensured. The developed
methodology is validated in direct switching control of a power amplifier for
high-precision motion systems, where it significantly improves the steady-state
output current ripple.
