This paper introduces the notion of w-stability of feedback systems. This is a generalization of a concept of well-posedness discussed by Willems. w-Stability requires that a feedback system should remain stable under a certain class of perturbations which may not be vanishingly small when measured by the gap metric. The paper derives necessary and sufficient conditions for a feedback system to be w-stable. Further, an investigation of well posedness is given for feedback systems where high frequency roll-off has been suppressed for modelling simplicity. This question is pertinent in standard PID control.
- PID control
- modelling uncertainty