1. The problem statement, all variables and given/known data The state space model of a nonlinear system is [tex]x'_1(t) = 2x^2_2(t) - 50[/tex] [tex]x'_2(t) = -x_1(t) - 3x_2(t) + u(t)[/tex] Where [tex]x_1(t)[/tex] and [tex]x_2(t)[/tex] are the states, and u(t) is the input. The output of the system is [tex]x_2(t)[/tex]. Find the state space model of this system linearized at the equilibrium point (-15, 5) 2. Relevant equations State space modeling, Jacobian Matrix(?) 3. The attempt at a solution I think my attempt lies on false assumption, but here's what I did. Since we're linearizing at a known equilibrium point for a nonlinear system, and since [tex]x'_1(t) = 2x^2_2(t) - 50[/tex] contains non linear term, we must first take a derivative of it as denoted in Jacobian matrix. derivative of x_1(t) is [tex]x''_1(t) = 4x_2(t)[/tex] So the state space model we get is [x'_1] = [ 0 4 ] [x_1] + [ 0 ] u(t) [x'_2]aa[-1 -3 ] [x_2] a[ 1 ] (Sorry I have no clue how to put this matrix in Latex). But then how do we get the output from this state space model?