Design of Robust SISO Controllers for Stable Plants Using FIR Q Parameters

The tradeoff between performance and robustness in single-input single-output linear time-invariant stable plants represents a fundamental aspect of robust control design. We use a theorem that clearly exposes such a tradeoff between the maximum magnitude of the additive plant uncertainty and the performance weighting function in the frequency domain as a basis to design robust controllers with finite impulse response Q parameters. The optimal controller is given in the theorem in the form of the frequency response of a Q parameter of an internal model control structure. The design and tuning of the robust controller relies on an approximate solution to a frequency response fitting problem solved over the class of discrete-time finite impulse response Q parameters via the solution of a linear matrix inequality problem.