Page 733 - Mechanical Engineers' Handbook (Volume 2)

724 State-Space Methods for Dynamic Systems Analysis

Table 1 (Continued)
System matrices
I 0 n
00 0 0 0
n
1
A 1 B 1

n 1
n 1
nn 1
n 1
C [00. . .01] D n
III. Normal or diagonal Jordan canonical form
Related conditions
(i) Characteristic equation roots s i , i 1, .. ., n, are real and distinct
Simulation diagram

System matrices
s 1 s 2 0
1
1
A B
0 s n 1
... K ]
C [K 1 K 2 D K 0
n
where K 0 lim [H(s)] and K i lim [(s s i )H(s)] i 1, .. ., n
s→ s→s i
IV. Near-normal canonical form
Related conditions
(i) One pair of complex conjugate characteristic equation roots

k
s s js ki
kr
kr
s k 1 s js ki