Homework #8
1.
Consider the state equation 
, where
,
which was obtained by linearizing
the nonlinear equations of motion of an orbiting satellite about a steady-state
solution. In the state 
, x1 is the perturbation in the radius,
while x3 is the perturbation in the angle. In the input vector 
, u1 is the radial trust and u2
is the tangential thrust.
a) Is the system controllable from u? If
,
is the system observable from y?
b) Can the system be controlled if the radial thruster fails? What if the tangential thruster fails?
c) Is the system observable from y1 only? From y2 only?