  A state observer design for the inertia wheel pendulum considering static
friction of the actuated inertia disc is presented. The frictional force is
modeled by the Stribeck effect, with two separate differential equations
describing the sticking and non-sticking system, respectively. The transition
between the two scenarios is in general determined by a static friction
condition. Three proposed observers are designed for both the sticking and
non-sticking model. Depending on the probability of the respective model given
a current measurement, the more likely is selected for state estimation. The
performance is demonstrated on a laboratory demonstrator, where the observers
including the proposed probabilistic model selection are compared.
