Linearizing ordinary differential equations

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SUMMARY

The discussion focuses on the process of linearizing coupled non-linear ordinary differential equations (ODEs) using partial derivatives and the Jacobian matrix. The user seeks clarification on the state-space model of the Jacobian matrix, indicating a lack of accessible references on this specific transformation. The inquiry highlights the need for a deeper understanding of the state-space representation in the context of ODE linearization.

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  • Understanding of ordinary differential equations (ODEs)
  • Knowledge of partial derivatives
  • Familiarity with Jacobian matrices
  • Basic concepts of state-space models
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  • Research the derivation of state-space models for non-linear systems
  • Study the application of Jacobian matrices in linearization techniques
  • Explore resources on the linearization of ordinary differential equations
  • Investigate advanced texts on control theory and state-space representations
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Mathematicians, engineers, and researchers working with differential equations, particularly those involved in control systems and dynamic modeling.

thavamaran
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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!
 
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