Nonlinear Systems/Differential Equations

Linearization

Jacobian

 

 

Tool:      The Jacobian is a matrix whose entries are derivatives of autonomous differential equation functions with respect to state variables evaluated at point x₀:

     

Note:      Take the partial derivative first. Then plug in .

Note:      Each function, ƒ_i, is a function of state variables x₁,...,x_N.