The disturbance decoupling problem for jumping hybrid systems

The problem considered here consists in decoupling the output of a hybrid system from an unknown disturbance by means of state feedback, while assuring global asymptotic stability of the closed-loop dynamics. The considered hybrid systems are characterized by the coupling of a linear flow dynamics with a discontinuous jump dynamics. Suitable geometric methods and tools are introduced and, assuming that the linear flow dynamics is reachable, a general sufficient solvability condition is given. A more restrictive sufficient solvability condition that can be checked by a simple, finite procedure is also given. This provides a practical way to construct solutions in many situations.