A further note on overshoot estimation in pole placements

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.