thavamaran
- 39
- 0
Hi guys, I am trying to linearize a coupled non-linear ode. I used partial derivative, and then jacobian matrix, i have seen paper using state-space model of jacobian matrix. I can't get a proper reference on this state-space model.
Attached is the non-linear ode, the partial derivative of the non-linear ode and the state-space model of jacobian matrix.
Can someone enhance or explain how they got the state-space model as the transformation, is it a fix formulation. Sorry for asking this way cause I can't find any books or reference referring or explaining this. Please help me! thanks!
Attached is the non-linear ode, the partial derivative of the non-linear ode and the state-space model of jacobian matrix.
Can someone enhance or explain how they got the state-space model as the transformation, is it a fix formulation. Sorry for asking this way cause I can't find any books or reference referring or explaining this. Please help me! thanks!
Last edited:
![Three numbered differential equations (1) to (3): dN(t)/dt = I(t)/(q·V_a) − g₀[N(t) − N₀]·S(t)/(1 + ε·S(t)) − N(t)/τ_n; dS(t)/dt = Γ·g₀[N(t) − N₀]·S(t)/(1 + ε·S(t)) − S(t)/τ_p + Γ·β·N(t)/τ_n; dφ(t)/dt = ½α[Γ·g₀[N(t) − N₀] − 1/τ_p].](/data/attachments/23/23553-5e736276d11308fe5972e84cba7a8023.jpg?hash=XnNidtETCP)
![Equations (7) to (11): partial derivatives of dN/dt and dS/dt with respect to N and S, forming a Jacobian matrix in a state-space model with input I(t) and output y = [0 1][N S]^T.](/data/attachments/23/23554-583f5cfa23ebe152e3a1abef2928d691.jpg?hash=WD9c-iPr4V)