Design of a Linear Controller for Robust Tracking and Model Following

We consider a class of linear systems in which there is time-varying uncertainty. These linear uncertain systems can be divided into two types. Systems in which the structure of the uncertainty satisfies certain matching conditions are called matched, and those systems in which the uncertainty does not satisfy the matching conditions are called mismatched. A linear control law is determined which produces tracking of dynamic inputs. The tracking error does not asymptotically decrease to zero because the systems are uncertain, instead the error is bounded. In the case of matched systems this error bound can be made arbitrarily small, and the system is said to practically track the input. In mismatched systems, the tracking error cannot be made arbitrarily small, and the system is said to ε-track the input. Previously published theory requires nonlinear controllers for practical tracking. Here, we derive a linear feedforward control law. Several examples illustrate the results.