A new metric for stability robustness

This paper seeks to combine two concepts in mathematics, namely, arcwise connectivity and subspace gap, and propose a new metric for stability robustness analysis of linear time-invariant finite-dimensional control systems. This new metric is shown to possess the desired qualitative properties for the analysis of stability robustness and computational simplicity as well. Compared with the gap metric and pointwise gap metric, the distinct features of the new metric are that it can be used: to derive a necessary and sufficient condition on robust stability, to yield the same problem of robustness optimization for designing stabilizing controllers, to describe a larger class of perturbed plants, and to provide tighter estimates on stability robustness