Output Feedback Control and Robustness in the Gap Metric

Design and robustness of output derivative feedback stabilization, lambda-tracking and funnel control for linear MIMO-systems is analysed. These control strategies require only structural assumptions of systems: relative degree and normal form, minimum phase and positive high-frequency gain. A detailed analysis of this properties is given for MIMO-systems with non-strict relative degree. The contollers are robust in this sense: if a closed-loop system [P,C] (applying controller C to linear plant P) is stable and the gap metric between P (or C) and a plant P1 (or controller C1) is sufficiently small, then the closed-loop system [P1,C] (or [P,C1]) is again stable. In particular: output derivative feedback may be replaced by output delay feedback (approximations of the derivatives), provided the delay is small. Lambda-tracking and funnel control may be applied to systems which are close (in terms of a small gap) to systems satisfying the above structural assumptions.