ROBUSTNESS WITH RESPECT TO DELAYS FOR EXPONENTIAL STABILITY OF DISTRIBUTED-PARAMETER SYSTEMS

In this paper we address the question of whether the open-loop exponen tial growth rate of a linear system can be improved by a feedback in s uch a way that this improvement is robust with respect to small delays in the feedback loop. When the input operator is admissible, and the class of possible feedbacks consists of compact operators, we find tha t if a feedback can improve the exponential growth rate, then it can d o so robustly. Furthermore, we find that if the control space is finit e dimensional and a bounded feedback cannot be found to improve expone ntial stability, then a large class of unbounded feedbacks cannot impr ove the exponential growth rate robustly, even if such feedbacks can i mprove the exponential growth rate in the absence of delays.