Quiz 2

\underline{Problem 1}: Consider the following dynamic system:

\frac{d}{dt} [ \begin{matrix}x_{1} \\ x_{2} \end{matrix} ] = [ \begin{matrix}x_{1}^{2} − x_{2} + u \\ e^{x_{2}} − 3 \end{matrix} ]

If the steady state value of the input is u_{s} = 1, what are the steady state values of the states, x_{1s} and x_{2s}. Linearize the system around these steady state values.