Page 745 - Mechanical Engineers' Handbook (Volume 2)

736 State-Space Methods for Dynamic Systems Analysis

Table 3 (Continued)
V. Nondiagonal Jordan canonical form
Related conditions
(i) One real characteristic equation root z k repeated m times
(i.e., z k z k 1 z k m 1 ).
(ii) All other roots are real and distinct.
Simulation diagram

System matrices

0
z 1 1
0 0
0
z k 1
1
z 1 0 0
k
F 0 1 0 G
0 z k 1
1
z k m
0
0 0
0 z n 1
C [K 1 ... K k 1 K k1 ... K km K k m ... K ] D K 0
n
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 m,.. ., n
1 d j 1 [(z z ) H(z)]
and K k m j 1,..., m
kj
(j 1)! js j 1
z z k