Satriani indeed did teach Mr Vai amongst others... I think the list includeds Kirk Hammet as well!
Satriani has been playing Ibanez guitars for as long as ive been a fan (1990 ish) and maybe a few years before this.
His range of Signature guitars include:
JS100 (This is the cheap Korean Made Model)
JS1000
JS1200
JS1600
Satch also uses/ endorses the following:
Vox Pedals
Peavey Amps
Planet Waves items (straps, picks)
I have heard a rumour that he nonger uses the Peavey amps that he helped design, but has gone back to using Marshalls!
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Ibanez JS1000 Black Pearl Finish, Peavey JSX 120 Head, TC Electronic G System, Marshall 1936V Cab, MXR Zak Wylde OD, Marshall Bluesbreaker MK2, JD Cry Baby Wah from Hell, Boss FV500L and FV500H