A further note on overshoot estimation in pole placements  

作　　者：Zhijian JI Xiaoxia GUO Shixu XU 

机构地区：[1]School of Automation Engineering, Qingdao University, Qingdao Shandong 266071, China [2]Department of Mathematics, Ocean University of China, Qingdao Shandong 266071, China

出　　处：《控制理论与应用（英文版）》2007年第1期57-59,共3页

基　　金：This work was supported by the National Natural Science Foundation of China (No. 60604032, 10601050).

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.

关 键 词：Linear system Transition matrix OVERSHOOT 

分 类 号：O231.1[理学—运筹学与控制论]