Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 8
Situational Awareness; Troubleshooting
ATC Issue All Types; Conflict Airborne Conflict
General None Reported / Taken
Airspace Structure; Human Factors
I was working Aircraft X as a visual approach to PSP. They were cleared about 15-20 miles NE of the airport. I noticed a 'Z' tag (PSP Tower) on a downwind departure that was moving quickly; so it caught my attention. I clicked on it to see that it was the local [aircraft type]; Aircraft Y.  This aircraft is notorious in our area for getting in the way of IFR arrivals to PSP; so I kept my eye on the data tag.Aircraft Y dropped off the Z tag and turned southbound after passing an arrival to 31L. This put them on a converging course with Aircraft X. I still had some altitude separation to work with; so I called traffic to Aircraft X and told them to stop at 045 since Aircraft Y appeared to be momentarily level at 040. I thought maybe Aircraft Y saw the arrival. After I stopped Aircraft X; tower called and said Aircraft Y had Aircraft X in sight. I then saw Aircraft Y start climbing; and issued a traffic alert to Aircraft X. At the same time Aircraft X started descending.Aircraft Y was never pointed out to me; and no coordination was performed by the tower. Aircraft Y pilot is notorious in our area because they fly around at high speed; in highly congested areas; doing aerobatic maneuvers without talking to anyone. Then they fly back in the PSP; skipping approach every time; avoiding any sequencing from us. They force us to move around them; since we don't know what their intentions are; and then call the tower right before the Delta to get pattern entry instructions. This is all legal; but unsafe. The plane is from a local area; and they are very aware of the procedures and traffic in the area. However; they continue to avoid talking to approach control because it is not required in a TRSA.The few times the pilot has been on approach frequency; they are argumentative and obviously frustrated with our instructions.  The safety culture has obviously left this pilot and they feel they are above the rest of us and our mission of safe and efficient flow.The issue in this event is the conflict happened right outside the delta; with no coordination; and probably some pressure from the pilot to get on course and on their way. The Tower probably felt pressure to terminate the aircraft; as they were already outside of their delta airspace; and the TRSA has no requirements for participation.PSP airspace needs a Class Charlie or Bravo airspace around it. We provide no protection to a steady stream of arrivals by having a voluntary participation airspace surrounding it. The airspace is BUSY. The controllers have no safe airspace to assume separation. Aircraft fly through our arrival and departure corridors at leisure; stopping departures; corrupting sequences and causing unstable or aborted approaches.UDD is located about 10 miles east of PSP and has VFR jet departures launching all day long; right at aircraft in the downwind for PSP. What major airport allows for aircraft to fly into the radar downwind?  This creates an incredibly confusing situation for the controller; as we have no idea what the intentions are of any of the aircraft. When you look at the amount of traffic; the speed; and the lack of maneuvering room; the Springs/Desert sector is a time bomb waiting to explode. We as controllers do the best we can to alleviate these situations; but with mountains surrounding almost all quadrants of the valley; there are few routes to take in and out; which results in many head-on situations.I have a similar report that I filed a few years ago where a YAK converged with an arrival for PSP 13R and the pilot reported a NMAC with the aircraft.  Protected Class Charlie or Bravo airspace would have avoided both of these situations. The controllers and pilots deserve to be afforded some level of protection when close into the airport. RA's and and NMAC's 5-10 miles away from a major airport are unacceptable.
SCT TRACON Controller reported a conflict between an IFR arrival and a high speed highly maneuverable aircraft just clear of the PSP Class Delta/TRSA.