ERJ 190 Pilot reported the loss of #2 Hydraulic System on climb out. The flight crew requested priority handling and performed an air turn back and precautionary landing at departure airport.

Narrative

During cockpit flow; hydraulic systems pages appeared within normal quantity. Thirty minutes into the flight we received a HYD 2 LO QTY. The HYD 2 LO QRH was run. The quantity was at 16%; pressure 2;900 psi; and temperature around 28C. Upon contacting Dispatch and Maintenance via AIRINC; the decision was initially made to continue to ZZZ1 due to a suspected faulty sensor. During the discussion the HYD 2 quantity slowly fell to 0%. Roughly 5 minutes after the quantity was at 0% the HYD 2 pressure dropped from 2;900 psi slowly to 2;500 psi and then rapidly to 0 psi. At this point; Maintenance was in agreement that the HYD 2 SYS was lost. The decision was made to [request priority handling] and return to ZZZ.Shortly after HYD 2 LOW PRESS EICAS appeared and corresponding QRH was completed. [Cabin Crew] was informed of the situation and code yellow. Customers were informed of the problem and of a return to ZZZ with roughly 20 minutes remaining in flight. During the descent with FO (First Officer) flying; the aircraft was configured at 300 kts.; autopilot on; descending through mid twenties at 2;000 FPM; on LNAV with a straight course. The aircraft was rolled sharply in an uncommanded right roll of 5-15 degrees. This occurred twice. AP TRIM MISMATCH was displayed and FO ran appropriate QRH. At this point the decision was made to hand fly the arrival and I took control to allow FO to review QRH and special considerations for landing. Aileron trim was used to compensate roll with maximum trim roughly 1.5 ticks to the right. Sudden unannounced rolls continued with the last being at around 200 ft. AGL. HYD SYS page was continuously monitored and it appeared rolls were linked to a surge in PSI which ranged from 0-1;000 psi. We had an uneventful flaps full landing on XXL. The left engine TR (Thrust Reverser) was deployed. Directional control was not a problem. Around 40 kts.; brake pressure increased unexpectedly and the aircraft jolted. Aircraft came to stop on XXL. CFR (Crash Fire Rescue) inspected brake temperatures which were 260/30 30/460+. CFR cleared aircraft to be towed to Gate XX. Customers deplaned uneventful.