Dua in Sujood (Sunnah prayer & Qiyam)?

Salamualaikum my dear brothers/sisters in Islam. I'd like to know if it is permissible to make dua in Sujood in Sunnah prayers. E.g. 4 rakaah Sunnah prayer before Zuhr. Can I make dua in the 4th rakaah's last Sujood after reciting Subhan'ala rabbiyal a'ala x3? Regarding Tahajjud prayer. I pray 2 rakaah and sometimes 4 (Tasleem after 2 rakaahs). Is there anything wrong if I supplicate in the 2nd rakaah Sujood of my Tahajjud prayer? i.e. In the 1st rakaah's sajda I say Subhan'ala rabbiyal a'ala x3 then I get up. In the 2nd rakaah's sajda I say Subhan'ala rabbiyal a'ala x3 then I supplicate in arabic as well as in my native language. Is my procedure correct? Please help me out. I'm very much eager to know. As i'm confused regarding this issue. Jazakallah Khair.