摘要
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 x = (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 by 1/2 (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.
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 x = (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 by 1/2 (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.
基金
This work was supported partly by the Chinese National Natural Science Foundation. The work of Wang was also supported partly by the US National Science Foundation (No. DMS - 0072620).
