Template:ETH Sensitivity Matrices
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Since we are interested in the output sensitivities at steady state, we set <tt>dS(t)/dt = 0</tt> and can solve for S: | Since we are interested in the output sensitivities at steady state, we set <tt>dS(t)/dt = 0</tt> and can solve for S: | ||
| - | S = J<sub>x</sub> \ J<sub>p</sub> | + | S = − J<sub>x</sub> \ J<sub>p</sub> |
\ : matrix left division | \ : matrix left division | ||
Latest revision as of 08:11, 31 October 2006
To analyze the sensitivity of the system for all concerned parameters, we compute the sensitivity matrix S:
S = (∂x/x) / (∂p/p) = (∂x/∂p) * (p/x) S : sensitivity matrix, #x rows, #p columns x : states (concentrations) p : parameters
We use jacobian matrices of the system equations to compute the sensitivity matrix S. We therefore augment the set of differential equations by
dS(t)/dt = Jx(t) S(t) + Jp(t) Jx(t) = ∂f(x,p,t)/∂x Jp(t) = ∂f(x,p,t)/∂p
Since we are interested in the output sensitivities at steady state, we set dS(t)/dt = 0 and can solve for S:
S = − Jx \ Jp \ : matrix left division
