Robust output feedback control against disturbance filter uncertainty described by dynamic integral quadratic constraints

Motivated by a robust disturbance rejection problem, in which disturbances are described by an uncertain filter at the plant input, a convex solution is presented for the robust output feedback controller synthesis problem for a particularly structured plant. The uncertainties are characterized by an integral quadratic constraint (IQC) with general frequency‐dependent multipliers. By exploiting the structure of the generalized plant, linear matrix inequality (LMI)‐synthesis conditions are derived in order to guarantee a specified ??₂‐gain or ??₂‐norm performance level, provided that the IQC multipliers are described by LMI constraints. Moreover, it is shown that part of the controller variables can be eliminated. Finally, the rejection of non‐stationary sinusoidal disturbance signals is considered. In a numerical example, it is shown that specifying a bound on the rate‐of‐variation of the time‐varying frequency can improve the performance if compared with the static IQC multipliers. Copyright © 2009 John Wiley & Sons, Ltd.