Robust steady-state tracking

This paper addresses the robust performance problem when the performance measure is the “steady-state” value of an error signal. Necessary and sufficient conditions are derived for robust steady-state tracking of fixed inputs in the presence of structured time-varying uncertainty are derived. These conditions are easily computable and fit well with existing conditions on stability robustness and performance robustness when the performance measure is the level of disturbance rejection. Using these conditions, it is shown that time-varying perturbations of a nominal linear time-invariant plant can result in large steady-state tracking errors to fixed inputs even if the nominal plant and controller give zero steady-state tracking errors. The derived expressions for the worst-case steady-state tracking error give insight into how the time variation in the plant affects tracking errors and suggest that certain transfer function norms should be minimized to reduce the effect of these perturbations on the steady-state value of error signals