Recent Results on Time-Delay Systems by Emmanuel Witrant Emilia Fridman Olivier Sename & Luc Dugard

Author:Emmanuel Witrant, Emilia Fridman, Olivier Sename & Luc Dugard
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

hence all these parameters may be considered small. The “reduced order” system will be

(8.13)

A straightforward computation will give

(8.14)

where and are solutions of the following system of ordinary differential equations

(8.15)

If we check the inherent stability of (8.15) i.e. with all input signals identically 0, the following characteristic equation is obtained

(8.16)

where all coefficients are positive. Moreover it is easily obtained that this equation has a zero root and the other ones are in . If the boundary dampings , are neglected then (8.16) becomes

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