Sub/ triangle

I have a pair of the infamous Titus 202, using an inexpensive Yamaha sub. Up grading the sub would make a difference? I hear so much about speed, fast etc? I wonder if I can maximize the potential of the 202s by using a different sub... The room is 9x13. Thank you.
Tell us how you have the sub wired into your system , as well as, your other components.

What is it that's bothering you with your current system?

The Titus is a small speaker with a small woofer, so you'll get the best from them by moving the bass load to a subwoofer.
+1 Mr. Reynolds. There seems to have been a great deal of subwoofer talk centering around the term 'speed.' Personally, I have yet to see a measurement or experienced even very modest subwoofers that reacted slowly to a given input signal.

Out of phase recordings are notorious for putting the subs driver out of sync with the recording. IMO having the ability to invert phase via remote control at the listening position is a must.

There are many other aspects of subwoofer design, performance, and control, that could easily fill the taste and requirements of individuals as well as making their integration more seemless.
I have Triangle Titus also. Wonderful speakers that do what they do very well, but low bass extension is not what they do, so generally a very good candidate to supplement via sub(s).

If you do not care about or need bass extension below 50hz or so to be happy, I'd go sans sub with the Titus and get them to shine as is.

If more full range sound is the goal, I'd focus first what is needed to get sub integrated a best as possible for best sound without "muddying the waters".

From there, I would think about using two matching subs in order to help normalize bass response throughout the room further is bass is good in one listening position but not so much in others. Next step beyond that for same reasons would be to add additional subs, but benefits become increasingly marginal from there.
Probably go with Sunfire JR. sub...or small HSU...something known for speed and clarity...which is the signature French sound
Yes, speed and clarity is a common attribute of French speakers I have heard, mainly Triangle and Focal. They tend to sound more like planars or eletrostats in this regard than do many other box speaker designs.

Focal makes subs. Probably not a bad place to look, though I do think a lot of speed and clarity issues with subs has more to do with proper setup and integration with the mains than any inherent flaw in most good subs from reputable companies.

I suspect damping is a good thing to consider for speed and clarity with many powered subs. Many high power powered subs use Class D amplifiers nowadays, which tend towards higher damping and associated attributes of speed and clarity. THat bodes well I would think for using many different makes of modern powered sub effectively with speakers like the Triangles when needed.

Bass integration with hybrid speakers like Martin Logan is a common cited issue. Maybe ML might be a logical place to look for a sub in the case of Triangles as well?

I used my Triangle Titus XLs with an older M&K V1b sub for many years with good results up until the sub went up recently, and I have not done much research to date to investigate eventual possible replacement options. SO I am also interested in what people have to say about subs that might work particularly well with Triangle Titus speakers.