A Note on Overshoot Estimation in Pole Placements
  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. 
D. Cheng, L. Guo, Y. Lin, Y. Wang