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		Daizhan CHENG,Lei GUO,Yu,an LIN,Yuan WANG.[en_title][J].Control Theory and Technology,2004,2(2):161~164.[Copy]

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DaizhanCHENG,LeiGUO,YuandanLIN,YuanWANG
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Received:May 20, 2004

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A note on overshoot estimation in pole placements

Daizhan CHENG, Lei GUO, Yuandan LIN, Yuan WANG

(Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China ;Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA)

Abstract:

In this note we show that for a given controllable pair (A, B) and any λ>0, a gain matrix K can be chosen so that the transition matrix e~((A+BK)t) of the system =(A+BK)x decays at the exponential rate e~(-λt) and the overshoot of the transition matrix can be bounded by Mλ~L for some constants M and L that are independent of λ. As a consequence, for any h>0, a gain matrix K can be chosen so that the magnitude of the transition matrix e~((A+BK)t) can be reduced by1/2 (or by any given portion) over [0, h]. An interesting application of the result is in the stabilization of switched linear systems with any given switching rate (see [1]).

Key words: Linear system Transition matrix Squashing Lemma