The linearized equations of motion for a satellite are where

:X= Ax+Bu y = Cx+Du A= r 3~~ 2 ~ ~ 2~ 1 r ~ ~ 1 [ 1 0 0 0 J 0 01 'B= 00 'C= 0010'

-2w 0 0 0 1 D= [OJ The inputs u 1 and u 2 are the radial and tangential thrusts, the state variables x1 and x2 are the radial and angular deviations from the reference

(circular) oTbit, and the outputs y1 and y2 are the radial and angular measurements, Tespectively.

(a) Show that the system is controllable using both control inputs.

(b) Show that the system is controllable ·using only a single input. Which one is it?

(c) Sho·w that the system is observable using both measurements.

(d) Show that the system is observable us·ing only one measv.rement.

Which one is it 9 Problem