Recently, it is proved in the literature that for a given controllable pair (A, B) with A ∈ Rn×n, B ∈ Rn×m, and any λ≥1, a gain matrix K can be designed so that‖e(A+BK)t‖≤MλLe-λt, where M and L are constants independent of λ. Here, we show that M and L can be chosen much smaller than that proposed above. 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 existing result.
