  This paper considers an optimal impulse control problem of dynamical systems
generated by a flow. The performance criteria are total costs over the infinite
time horizon. Apart from the main performance to be minimized, there are
multiple constraints on performance functionals of a similar type. Under a
natural set of compactness-continuity conditions on the system primitives, we
establish a linear programming approach, and prove the existence of a
stationary optimal control strategy out of a more general class of randomized
strategies. This is done by making use of the tools from Markov decision
processes.
