CL650 FLT CREW EXPERIENCED LOST COM ENRTE TO HOU.

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WE DEPARTED LRD. THE CONDITIONS WERE VMC AT DEP AND TWR TURNED US OVER TO LAREDO DEP CTL SHORTLY AFTER TKOF. LAREDO DEP CLRED US TO FL330 AND CLRED US DIRECT TO HOU ARPT. THAT WAS OUR LAST CONTACT WITH ANY CTLING FACILITY. AFTER PASSING FL230 AND NOT HEARING ANYTHING FROM DEP; WE TRIED TO CONTACT THEM TO ASK FOR OUR NEXT FREQ WITH NO JOY. WE SQUAWKED 7600 ON OUR XPONDER AND CONTINUED ON OUR RTE AS LAST CLRED. WE KNEW THAT HOU WAS VMC SO WE DECIDED TO CONTINUE TO OUR DEST ARPT. WE XMITTED IN THE BLIND THE ENTIRE REST OF THE FLT. WE ALSO TRIED TO XMIT ON THE COM AND RECEIVE OVER THE NEAREST APPROPRIATE VOR FACILITY WITH RECEPTION CAPABILITIES. I AM VERY FAMILIAR WITH THE ARRS AND APCHS TO THE ARPT. I HAVE FLOWN THIS RTE MANY TIMES BEFORE AND AS SOON AS WE ARE GIVEN TO ZHU THEY CLR US DIRECT TO LISSE FOR THE LISSE 6 (LISSE.LISSE6) ARR INTO HOU. I WANTED TO GIVE ZHU AND APCH CTL AS MUCH NOTIFICATION AS I COULD ABOUT THE RTE WE WERE FLYING; SO I OPTED TO GO DIRECT TO LISSE INTXN WHICH WAS IN OUR FLT PATH WITH THE XING RESTR OF 10000 FT. NORMALLY WHEN WE ARE HANDED OVER TO HOU APCH THEY CLR US ON A HDG OR DIRECT TO THE INITIAL APCH FIX FOR THE ILS TO RWY 12R OUT OF THE SMOAK INTXN AT HOU. I PROCEEDED DIRECT TO THE JABBS INTXN (THE INITIAL APCH FIX) AFTER SMOAK FOR THE ILS TO RWY 12R. AFTER BEING ESTABLISHED ON THE ILS TO RWY 12R WE RECEIVED A STEADY GREEN LIGHT SIGNAL FROM THE TWR CLRING US TO LAND. WE HELD OUR POS OFF THE RWY AND WAITED FOR ARPT OPS TO ESCORT US BACK TO GATE. ARPT OPS GAVE ME THE PHONE NUMBER TO HOU APCH CTL; WHICH I CALLED AFTER LNDG. APCH CTL SAID THAT THEY KNEW WHAT WE WERE DOING IN PROCEEDING TO THE LISSE INTXN. HE HAD NO COMPLAINTS AND GAVE ME THE PHONE NUMBER TO ZHU.