Analysis and Design of Delayed Genetic Regulatory Networks by Xian Zhang & Yantao Wang & Ligang Wu

Author:Xian Zhang & Yantao Wang & Ligang Wu
Language: eng
Format: epub
ISBN: 9783030170981
Publisher: Springer International Publishing

(4.10)

Proof

For an arbitrary piecewise constant switching signal , let denote the switching points of . For any but fixed , it is clear that for some nonnegative integer l. Choose the LKF of the following form:

(4.11)

with

where and are real matrices satisfying (4.7) and (4.8).

Then, along the solution of system (4.2), we have from (4.6) that

(4.12)

(4.13)

(4.14)

Applying Lemma 1.​16, we obtain

and

This, together with (4.14), implies that

(4.15)

Moreover, one can obtain from (4.3) that

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