摘要
Recently, it is proved in the literature that for a given controllable pair （A, B） with A ∈R^n×n, B ∈R^n×m, and any λ ≥ 1, a gain matrix K can be designed so that ‖e^（A＋BK）t‖ ≤Mλ^Le^-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.
Recently, it is proved in the literature that for a given controllable pair （A, B） with A ∈R^n×n, B ∈R^n×m, and any λ ≥ 1, a gain matrix K can be designed so that ‖e^（A＋BK）t‖ ≤Mλ^Le^-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.
基金
This work was supported by the National Natural Science Foundation of China (No. 60604032, 10601050).
