A nonlinear state space model has the form
\begin{bmatrix} \frac{dx_1}{dt}\\frac{dx_2}{dt}\end{bmatrix} = \begin{bmatrix} -x_1(t) - x_1(t)x_2(t) + 2\-x_2(t) + u(t) \end{bmatrix}
Which of the following statements is true?

Question

A nonlinear state space model has the form 
  \begin{bmatrix} \frac{dx_1}{dt}\\frac{dx_2}{dt}\end{bmatrix} = \begin{bmatrix} -x_1(t) - x_1(t)x_2(t) + 2\-x_2(t) + u(t) \end{bmatrix} 
 Which of the following statements is true?

Accepted Answer

If   u(t)=1  for all   t  then the system has an equilibrium point at   (x_1,x_2) = (1,1)

Answer

The system does not have any equilibrium points.

Answer

If   u(t)=1  for all   t  then the system has an equilibrium point at   (x_1,x_2) = (0,2)

Answer

If   u(t)=0  for all   t  then the system has an equilibrium point at   (x_1,x_2) = (1,1)

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A nonlinear state space model has the form \begin{bmatrix} \frac{dx_1}{dt}\\\...

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