1) A linear time-invariant system is described by the differential equation,
$\ddot{x} + 4\dot{x} + 8\dot{x} + 16x = 6u$
a) Let the state variables be defined as $x_1 = x$, $x_2 = \dot{x}$, $x_3 = \ddot{x}$ and output $y = x_1$. Write the state equations of the system in state-space form.
b) Find the characteristic equation by using state-space equation and then check the stability of the system.
Solution 1:
The Eigenvalues (poles) of the system are:
$s_1 = -4$, $s_2 = -0.5 + j2.4$, $s_3 = -0.5 - j2.4$
