An improved result on overshoot estimation

In (D. Cheng et. al, 2004),(D. Cheng et. al, 2005), it is proved that for a given controllable pair (A, B) with A isin Ropf^{n times n}, B isin Ropf^{n times m}, and any lambda > 0, a gain matrix K can be designed so that pare^{(A + BK)t} par les Mlambda^Le^-lambdat where M and L are constants independent of A. Here we show that M and L can be chosen much smaller than that proposed in (D. Cheng et. al, 2004),(D. Cheng et. al, 2005). As a consequence, the estimation on overshoot of a transition matrix can be bounded more precisely. This can be regarded as a complement to the result presented in (D. Cheng et. al, 2004),(D. Cheng et. al, 2005)