any one help me please?

sorry, it is not easy to see the relation between observer gain and time delay.

Please rephrase your question, I find it very unclear. That might explain why nobody answers.

thanks so much for replayed Mr  Zhengrong Xiang  and Mr Philippe Martin,( imean if the initial value of plant state different from initial value of observer state the error between observer state and state it large because the observer is not fast to reach the state ,

Hello,

I am still confused with your question.I understant you would like to estimate the state x of the model $\dot x=Ax+Bu$ from the knowledge of the known signals $u(t)$ (input) and $\bar y(t)$ (measured output). You can choose the matrix gain $K$, but as far as I understand, the actual implementation results in $\exp(A\Delta)K$ instead of $K$ (why is it so, and how is it connected to a time delay?).. Could you precise your overall problem, and also the size of $\Delta$ with respect to your problem time constants?

THanks @Philippe for replayed .