  A switched equilibrium of a switched system of two subsystems is a such a
point where the vector fields of the two subsystems point strictly towards one
another. Using the concept of stable convex combination that was developed by
Wicks-Peleties-DeCarlo (1998) for linear systems, Bolzern-Spinelli (2004)
offered a design of a state feedback switching rule that is capable to
stabilize an affine switched system to any switched equilibrium. The state
feedback switching rule of Bolzern-Spinelli gives a nonlinear (quadratic)
switching threshold passing through the switched equilibrium. In this paper we
prove that the switching threshold (i.e. the associated switching rule) can be
chosen linear, if each of the subsystems of the switched system under
consideration are stable.
