Question

Question 5: Consider the system: 4 28 -10 2 *60)15 -27*ces *[*]us, y=[-5 2]xV Check the controllability, the observability, the stability, the stabilizability and the detectability of the system. ok b) Determine which of the two modes of the system is not controllable. Is it possible to stabilize the system? AL) If u(t)=0, how would you choose x(0) to excite the first mode only. How would you choose x(0) to excite the second mode only. dd) Is x, = [ 13]" controllable? Justify your answer.

Answer 1

-13 YES2) Controllakt ty we chock entrollabiltyby ung tatman tot Dutt) - AR A = -1 35 29 1o AR -17 35 8-&$3 2 15 acl=2x16-65-0 The sy stem is un con trollakble Observobilty observabi ithy by usny katman's test Cnez -28 10 -4

1 &ol20 -20 0 The 4sem ic not ob serva ble that inding elgen vatu Stabilt ty we can chict 1CE-A3)=O 10 St -17 S-28 S+27 75 s-2) Cst2) +50 0 S=2,3 The eipen 3 in tv halt plane So the system unstable