  This paper treats the global stabilization problem of continuous-time
switched affine systems that have rank-deficient convex combinations of their
dynamic matrices. For these systems, the already known set of attainable
equilibrium points has higher dimensionality than in the full-rank case due to
the existence of what we define as singular equilibrium points. Our main goal
is to design a state-dependent switching function to ensure global asymptotic
stability of a chosen point inside this set with conditions expressed in terms
of linear matrix inequalities. For this class of systems, global exponential
stability is generally impossible to be guaranteed. Hence, the proposed
switching function is shown to ensure global asymptotic and local exponential
stability of the desired equilibrium point. The position control and the
velocity control with integral action of a dc motor driven by an h-bridge fed
via a boost converter are used for validation. This practical application
example is composed of eight subsystems, and all possible convex combinations
of the dynamic matrices are singular.
