Biologically motivated state space model

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joeseki

Joined Feb 25, 2012
1
I'm very rusty at my control theory.

could someone help me derive a state space model for the following problems:

1)
a molecular concentration is defined to be some function u(t)
u(t) drives some process to generate Xm(t)
Xm(t) generates Y(t)

2)
a molecular concentration is defined to be u1(t)
a 2nd molecular concentration is defined to be u2(t)
the 1st and 2nd molecule interact in some nonlinear fashion and this resulting process generates Xm(t)
Xm(t) generates Y(t)

I recall seeing a very nice presentation of transcription factor model converted into State Space, but I can no longer find the link. I wish I could remember the search criteria I used the first time.

My first guess at the state space model is as follows

1)
[Xm(t)] = Ax(t) + Bu(t)
Y(t) = Cx(t) + D

Where
[Xm(t)] is the first order change in X(t)
A, B, C are time invariant constants
D is noise in measurement

2)
I don't know how to do this one.
 
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