This paper investigates a procedure for on-line adaptation in linear control systems. This is accomplished by the use of a digital adaptive loop, which adjusts its parameters to satisfy a given performance measure. Few assumptions are made about the unknown parameters in the plant—only knowledge of loose bounds on the variations may be needed. Estimates are made of these parameters and the effects of the estimates illustrated. A simple example is presented to illustrate the adaption procedure and the performance of the system under such a procedure.