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Feedback Control in Systems Biology
book

Feedback Control in Systems Biology

by Carlo Cosentino, Declan Bates
October 2011
Intermediate to advanced content levelIntermediate to advanced
296 pages
9h 39m
English
CRC Press
Content preview from Feedback Control in Systems Biology
92 Feedback Control in Systems Biology
for some domain D R : x
e
D. To find a matrix P w hich satisfies these
conditions, we first apply the asymptotic stability conditions to the linearised
system
δ ˙x = A δx, where δx = x x
e
,
to get
V (δx) = δx
T
P δx > 0 (3.30a)
˙
V (δx) = δx
T
P δ ˙x + δ ˙xP δx
= δx
T
A
T
P δx + δx
T
P Aδx < 0 (3.30b)
Condition (3.30a) can be easily impos ed by requiring the matrix P to be
positive definite, that is
P > 0, (3.31a )
whereas condition (3.30b) is satisfied by any matrix P that satisfies the linear
matrix inequality
A
T
P + P A < 0. (3.31b)
The solution to the above set of L MIs can be calculated using standard opti-
misation packages (e.g. ...
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Publisher Resources

ISBN: 9781439816912