The cigenvalues of the system air -2 T- j equal t,o the diagonal elements of d.. Thc systcm does not ckimge its input-output hrliavior with thr tramformalion from Eq.. 0 0 b The proof i
Trang 1470 Apprritlix A Soltitions to tlic Excrcisc.:,
e== [ 1 3 - 8 j 1 3 t s j 1 d = 2
The cigenvalues of the system air -2 T- j (equal t,o the diagonal elements
of d) Thc systcm does not ckimge its input-output hrliavior with thr tramformalion from Eq 2.47 - 2.50
c) It, i s conLrollaI.)le as all elmwits of b are non-zero aiitl it is ohscrvable a.; all c.lernents of i: arc iion-zero
0 1 I 0 0
1 0 0 0 b) The proof i s easy if one recognises that left niultiplication with 1C-l can be intrrprf>tcd its horizontally mirroring the matrix elrinc'nts, and right iiiiilti- plication with T as vertical mirroring
Solution 3.1
Solution 3.2
a ) yes, b) no, c) no, (1) 110, e) yes, as H ( 5 = j 2 ) = 0
Solution 3.3
a ) Corisistmt norrrialisation for t hc components:
1
6 '
This yields Lhe iiorinalised component v:ihic+x R - 1; C = - L = 1.2