AUS CTLR EXPERIENCED OPDEV WITH ZHU WHILE TRYING TO ISSUE IFR CLRNC TO A C525 WHO OVERSHOT HIS ASSIGNED ALT.

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A C525 CALLED AUSTIN APCH ON FREQ 119.0 REQUESTING IFR CLRNC FROM GTU TO PNC. THE ACFT WAS AIRBORNE VFR ABOUT 8 MI N OF GTU. I INSTRUCTED THE ACFT TO MAINTAIN VFR AND SQUAWK THE BEACON CODE ON HIS IFR FLT PLAN. AUSTIN APCH CTLS N BOUNDARY IS JUST N OF GTU; SO I HAD TO COORDINATE WITH GRAY APCH CTL TO ISSUE THE IFR CLRNC IN THEIR AIRSPACE. AFTER COMPLETING THE 'POINT-OUT' TO GRAY APCH; I ISSUED THE CLRNC TO THE CITATION. WHILE READING THE CLRNC; THE ARTS DATA TAG WENT INTO 'COAST' MODE; AND I WAS UNABLE TO SEE THE MODE C READOUT; ALTHOUGH I KNEW THE ACFT COULD NOT BE MUCH HIGHER THAN 9000 FT OR SO; AS I SAW AN ALT OF 8000 FT SHORTLY BEFORE. AS THE PLT READ BACK THE CLRNC; THE ARTS DATA TAG REACQUIRED; AND I COULD SEE THE CITATION STILL HAD A GOOD CLB RATE GOING; APCHING 12000 FT. IN THE CLRNC I ORIGINALLY STATED 12000 FT; AND I AM NOT SURE WHAT THE PLT SAID DURING THE READBACK; BUT IT IS A MOOT POINT. I RESTATED 12000 FT AS SOON AS THE PLT FINISHED READING BACK HIS CLRNC. IT WAS TOO LATE; AS I OBSERVED THE MODE C GO TO 12700 FT. THIS VIOLATES ZHU AIRSPACE. THE ACFT DSNDED TO 12000 FT.