Control of an amplifying wave on an infinite continuum

Previous work on the space-sampled feedback control of continuum instabilities in flowing systems is extended. When the continuum over which control is desired is many wavelengths long, it is often convenient to construct the control system of many sampling stations, each approximately one wavelength in size. The stability of such a system is discussed, and a new type of instability is found which does not appear when the system is small in terms of a wavelength.