Pointwise minimum norm control laws for hybrid systems

Minimum-norm control laws for hybrid dynamical systems are proposed. Hybrid systems are given by differential equations capturing the continuous dynamics or flows, and by difference equations capturing the discrete dynamics or jumps. The proposed control laws are defined as the pointwise minimum norm selection from the set of inputs guaranteeing a decrease of a control Lyapunov function. The cases of individual and common inputs during flows and jumps, as well as when inputs enter through one of the system dynamics, are considered. Examples illustrate the results.