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		Zhijian JI,Xiaoxia GUO,Shixu XU.[en_title][J].Control Theory and Technology,2007,5(1):57~59.[Copy]

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ZhijianJI,XiaoxiaGUO,ShixuXU
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Received:November 04, 2005Revised:September 25, 2006

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A further note on overshoot estimation in pole placements

Zhijian JI, Xiaoxia GUO, Shixu XU

(School of Automation Engineering, Qingdao University, Qingdao Shandong 266071, China; Department of Mathematics, Ocean University of China, Qingdao Shandong 266071, China)

Abstract:

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.

Key words: Linear system Transition matrix Overshoot