Finite Dimensional Robust Controller Designsvia the Gap Metric

There are two schemes provided via the gap metric for designing finite dimensional robust controllers for distributed parameter LTI systems. The finite dimensional controllers designed according to these two schemes are guaranteed to stabilize the distributed parameter LTI systems and their neighborhoods, and the real closed-loop responses can be estimated via the designed ones. Several related problems are also addressed such as the continuity of the largest robust stability radius, the finite dimensional approximations in the gap metric, and the relationship between the largest robust stability radius of a system and that of its optimally robust controllers.