I am interested in designing a robust controller for a small satellite with antenna, sloshing propellant and flexible panels on board. I am mostly interested in achieving arcsec precision pointing given such a scenario. Avoiding microvibration and jitter analysis from reaction wheels.
Among Quantitative Feedback Theory and H infinity, which one is preferred for robust control of satellites esp. small satellites? And why?
First, you should define what you mean by "small satellite", the definition can vary between 30kg to 300kg.
Second, in a small satellite, panels are generally mounted over faces rather than on deployable surfaces to avoid flexible mode disturbance, also flexible modes are usually specified to exist only in high frequencies, partially due to launcher restrictions. You can have guidance laws that prevent high torques from exciting the first mode, but that basically means limiting acceleration when needed.
Antennas in most small satellites are not steerable because this kind of mechanical part is prone to failure.
Many "small" satellites have no propulsion, so no problem with sloshing either. Some of the one that do have fuel tanks with rolling diaphragm, so sloshing is severely attenuated as well.
Jitter is then mostly driven by reaction wheels, whose average speed in orbit requires very complex and mission specific analysis. However, jitter happens at high frequencies, above 100 Hz, while I'm yet to hear about any AOCS software running above 64Hz. Most of systems I know run at 10Hz or below. This means that no mater what control technique you are using, there is no way you can control jitter.
If you were to consider a large spacecraft such as GeoEye-1 then these techniques could be closer to making sense.
Finnally, "arcsecond accuracy" is with respect to what? An inertial direction or maybe a location on Earth? If it is the latter, there are many other error contributors, including but not limited to time synchronization on board and Earth ephemeris prediction and computation.
So case in point, unless you are working with an academic problem, I doubt you gain much from robust control theories. You might as well use them, but when you find yourself in times of trouble, mother Mary will likely tell you to redesign the spacecraft rather than change your control algorithms.