  Given a discounted cost, we study deterministic discrete-time systems whose
inputs are generated by policy iteration (PI). We provide novel near-optimality
and stability properties, while allowing for non stabilizing initial policies.
That is, we first give novel bounds on the mismatch between the value function
generated by PI and the optimal value function, which are less conservative in
general than those encountered in the dynamic programming literature for the
considered class of systems. Then, we show that the system in closed-loop with
policies generated by PI are stabilizing under mild conditions, after a finite
(and known) number of iterations.
