Stabilizability in impulsive optimization problems
We introduce the concepts of impulsive and of regular Sample and Euler stabilizability for impulsive control systems, where a cost is also considered. A condition guaranteeing the existence of a discontinuous stabilizing feedback such that the corresponding (impulsive or regular) sampling and Euler solutions have costs all bounded above by the same continuous, state-dependent function, is presented. This condition, based on the existence of a special Control Lyapunov Function, implies also that the infima of the cost over impulsive and over regular inputs and solutions, coincide.