On the maximum principle for impulsive optimal control problems with infinite time horizon

We consider optimality conditions for impulsive control problems, where time horizon is infinite and, besides time-continuous control, the time-instances and values of system trajectory jumps are chosen optimally. The maximum principle, including transversality condition, is proved for the concept of weakly overtaking optimality allowing for both finite and infinite values of objective functional. The special case of a periodic optimal solution is considered with an illustrative example.