Biologically motivated state space model

Discussion in 'Math' started by joeseki, Feb 25, 2012.

  1. joeseki

    Thread Starter New Member

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

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

    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)

    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

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

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

    I don't know how to do this one.