  Steady state multiplicity can occur in nonlinear systems, and this presents
challenges to feedback control. Input multiplicity arises when the same steady
state output values can be reached with system inputs at different values.
Dynamic systems with input multiplicities equipped with controllers with
integral action have multiple stationary points, which may be locally stable or
not. This is undesirable for operation. For a 2x2 example system with three
stationary points we demonstrate how to design a set of two single loop
controllers such that only one of the stationary points is locally stable, thus
effectively eliminating the "input multiplicity problem" for control. We also
show that when MPC is used for the example system, all three closed-loop
stationary points are stable. Depending on the initial value of the input
variables, the closed loop system under MPC may converge to different steady
state input instances (but the same output steady state). Therefore we
computationally explore the basin boundaries of this closed loop system. It is
not clear how MPC or other modern nonlinear controllers could be designed so
that only specific equilibrium points are stable.
