For　discounted　optimal　regulation　design,　the　stability　of　the　controlled　system　is　affected　by　the　discount　factor.　If　an　inappropriate　discount　factor　is　employed,　the　optimal　control　policy　might　be　unstabilizing.　Therefore,　in　this　article,　the　effect　of　the　discount　factor　on　the　stabilization　of　control　strategies　is　discussed.　We　develop　the　system　stability　criterion　and　the　selection　rules　of　the　discount　factor　with　respect　to　the　linear　quadratic　regulator　problem　under　the　general　discounted　value　iteration　algorithm.　Based　on　the　monotonicity　of　the　value　function　sequence,　the　method　to　judge　the　stability　of　the　controlled　system　is　established　during　the　iteration　process.　In　addition,　once　some　stability　conditions　are　satisfied　at　a　certain　iteration　step,　all　control　policies　after　this　iteration　step　are　stabilizing.　Furthermore,　combined　with　the　undiscounted　optimal　control　problem,　the　practical　rule　of　how　to　select　an　appropriate　discount　factor　is　constructed.　Finally,　several　simulation　examples　with　physical　backgrounds　are　conducted　to　demonstrate　the　present　theoretical　results.