Dynamic Systems with Time Delays: Stability and Control by Ju H. Park & Tae H. Lee & Yajuan Liu & Jun Chen

Author:Ju H. Park & Tae H. Lee & Yajuan Liu & Jun Chen
Language: eng
Format: epub
ISBN: 9789811392542
Publisher: Springer Singapore

Based on the above polynomials, the following triple-summation inequality is developed from Lemmas 4.6 and 4.7:

(4.31)

where

(4) (in the upper-triangular form)

In the quartic-summation inner product space with the inner product defined as , the following quartic-summation inequality is developed:

(4.32)

where

In the stability analysis for time-delay systems, the commonly encountered problem is to estimate summation terms such as . So, with x(i) being replaced by y(i) in (4.29), (4.30), (4.31) and (4.32) we get the following corollary.

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