One-tenth wavelength dipole, 1.9 GHz on FR4 PCB. About 10 mm long antenna?
Yes it is possible to design and impedance match a such antenna.
Anyone can do it. Very few can do it and get reasonable performance. Good skills how to set up a VNA is recommended as short antennas and extreme impedances both requires good calibration to be able to get useable results.
are there the other ways to match an impedance
Assume required matching circuit should cost less space on PCB then the antenna if it is somewhat balanced design? A few 0402 or 0201 inductors and capacitors is then all that you can fit in available space.
Make it simple and all you need is a 50 Ohm resistor for matching across antenna terminals. It would work just as good as a somewhat miscalculated design of a reactive network.
Do not know anything about this design concept except that it should have a small dipole antenna. Is it any reasons to prefer a dipole design over other alternative in this limited space?
Whole PCB size, is a bit bigger then 20 mm? For same antenna space will then a monopole perform much better and will be much easier to impedance match with discreet components. A monopole will probably also require fewer matching components for same result.
When it comes to very small compact PCB designs with printed antennas can even a loop antenna be to prefer from antenna efficiency view, as it can use else unused PCB space, such as edges around PCB and by this cost less PCB area and deliver better antenna efficiency.
As a reference, I did design a printed monopole 2.4 GHz, 2*9 mm occupied PCB area, relative wavelength a bit bigger then your antenna (relative wavelength) but still in the range of what I call a small antenna.
It was a real quickly designed antenna, easily done in 10 minutes and documented here:
https://www.antune.net/demo/bluetooth/index.html
This antenna was easy for me to design because I have the tools and know how to use them.
I can design a dipole, fitting in same space, but it would result in a less good antenna. Vast of time in my opinion.