All IIR filters introduce feedback - after all, that's the way they generate an infinite impulse response (hence the name). The output from an IIR filter is only bounded for a subset of possible inputs - it is possible to give input that will cause an IIR filter to go into self-sustaining oscillations.
That's why FIR filters are much more common in control systems. Unconditional stability is a big plus. FIR filters also have linear phase response. However, the transport delays introduced by an FIR filter can be problematic, too. FIR filters are easy to design, too - just do an inverse Fourier transform of the impulse response to get the frequency response, and vice versa.
Why use an IIR filter? An IIR filter with a given number of taps can be made to have much steeper roll-off than an FIR filter with the same number of taps. An IIR filter can be made to have lower transport delay, which could make or break a controller. Finally, if you really do want to produce oscillations under certain conditions, an FIR filter will never do that for you.
If you want to play with digital filter design a bit, you can download DFDP (an old Fortran program that runs under DOS). The next step up would be to use MATLAB Simulink's linear system analysis features to play around. If you're more serious about learning digital control system theory, the text you can't go past is Katsuhiko Ogata's Discrete-Time Control Systems (2nd Edition).