Solve this question from a system analysis worksheet

A certain dynamic system having a single input, $u(t),$ and a single output, $y(t),$ is

described by the following equations:

$p^{}=3pq+2p^2+2q-17$

$6q^{}+(4-8p)q^{}+(12+3p)q=u$

$y=p-q$

$($a$)$ Identify the state$-$variables involved in the system dynamics.

$($b$)$ Confirm that the above system has an equilibrium state at which $p=1$ and $q=3$

and identify the corresponding steady input and output values.

$($c$)$ Linearise the above model about the equilibrium state found in part $($b$).$ Report

the matrices $A,B,C,D$ for the state$-$space model and state clearly what

entries are found in the vectors of the state$-$space model.

$($d$)$ Explain what conclusions can be drawn from a state$-$space model in general.

Comment, if possible, on the stability of the system from part $($c$).$

$($e$)$ Construct a diagram showing how SIMULINK could be used to model the system

given.