Stability of Time-Delay Systems
Citations
3,748 citations
Cites methods from "Stability of Time-Delay Systems"
...R and a positive constant for which Vð Þ ð0Þk k2; dVðxtÞ dt )))) xt¼ ð0Þk k2; 8 2 C ½ max; 0 ;Rnð Þ where the (total) derivative is taken along solutions to (46). h To study the stability of (46), Yue et al. [78] use the following Lyapunov–Krasovskii functional: VðxtÞ ¼ xðtÞ0PxðtÞ þ Z t t max Z t s _xðvÞ0T _xðvÞdvds with symmetric matrices P 9 0 and T 9 0....
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...Naghshtabrizi and Hespanha [40] use the following Lyapunov–Krasovskii functional to analyze this system VðetÞ ¼ eðtÞ0P1eðtÞ þ Z t t max Z t s _e0ðvÞR _eðvÞdvds þ Z t t min e0ðsÞSeðsÞds where P1 9 0, R 9 0, S 9 0....
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...Theorem 14 Lyapunov–Krasovskii [13]: The DDE...
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...However, the Lyapunov–Krasovskii theorem generally leads to less conservative results....
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...This means that an NCS with a maximum number of consecutive dropouts equal to m is still a DDE like (46), (47), but with min :¼ min k2N f kg; max :¼ max k2N ftkþ1þm tk þ kþ1þmg: The Lyapunov–Krasovskii and the Razumikhin theorems [11], [13], [55] are the two main tools available to study the stability of DDEs of the form of (46) and (47)....
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Cites background or result from "Stability of Time-Delay Systems"
...(9) are set to zero, and Z='I (' is a suTciently small positive scalar), then Theorem 2 is identical to the well-known delay-independent stability criterion in and Gu et al. (2003) (Proposition 5....
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...Furthermore, the new criteria also contain the well-known delay-independent stability condition in Gu, Kharitonov, and Chen (2003) and Hale and Verduyn Lunel (1993)....
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...(9) are set to zero, and Z='I (' is a suTciently small positive scalar), then Theorem 2 is identical to the well-known delay-independent stability criterion in and Gu et al. (2003) (Proposition 5.14 on p. 169) and Hale and Verduyn Lunel (1993) (Eq....
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References
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"Stability of Time-Delay Systems" refers methods in this paper
...The matrix background for this section is readily found in many texts; we refer to Golub and Van Loan [81], Horn and Johnson [122]....
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