Biomedical Engineering Reference
In-Depth Information
FIGURE 4-19
S-plane showing the
criterion for system
stability.
If it is difficult to factorize the denominator, then it is possible to use the Routh-Hurwitz
criteria to determine the system stability (Raven, 1978). For the denominator written as a
polynomial
a
n
s
n
+
a
n
−
1
s
n
−
1
+···+
a
1
s
+
a
0
(4.78)
•
If any of the coefficients are negative, then the system will be unstable.
•
If any coefficient is missing then the system is, at best, critically stable.
Other criteria exist for stability, and it is suggested that the reader investigate these
further if they are of concern.
As illustrated in Figure 4-20, the actual time-domain response that occurs for an
impulse is a function of the position of the poles and whether they are real or complex.
FIGURE 4-20
Relationship
between pole
position and system
response.
