Bang-bang hybrid stabilization of perturbed double-integrators

A bang-bang hybrid controller is presented that globally practically stabilizes the origin of a double-integrator affected by an unknown bounded uncertainty at the input side. The proposed controller has two key features: it guarantees a uniformly bounded number of switches over any compact time interval, and it is robust against bounded measurement errors. When disturbances are absent, through a proper choice of the control parameters it reduces to the time-optimal bang-bang controller for the double-integrator.