In this note we show that for any given controllable pair (A,B) and any c> 1, a gain matrix K can be chosen so that the transition matrix of the system x' = (A+BK)x decays at the exponential rate exp(-ct) and the overshoot of the transition matrix can be bounded by Mc^L for some M and L that are independent of the choice of c.
Cite
@article{arxiv.math/0509705,
title = {A Note on Overshoot Estimation in Pole Placements},
author = {D. Cheng and L. Guo and Y. Lin and Y. Wang},
journal= {arXiv preprint arXiv:math/0509705},
year = {2014}
}