Page 744 - Mechanical Engineers' Handbook (Volume 2)

4 Solution of System Equations 735

Table 3 (Continued)
IV. Near-normal canonical form
Related conditions
(i) One pair of complex conjugate characteristic equation roots
z z jz ki
k
kr
kr
z k 1 z jz ki
(ii) All other roots are real and distinct.
Simulation diagram

System matrices

z 1 0 1
0 0
0 z k 1
1
0
z kr z ki
F 0 0 G
1
z ki z kr
1
0
z k 2
0 0
0 z n 1
where K lim [H(z)] K lim [(z z )H(z)]
i
0
i
z→ z→z i
i 1, k 1 and i k 2, .. ., n
1 1
k
k
K k1 2 –Im[(z z )H(z)] z z k K k2 2 –Re[(z z )H(z)] z z k