Stability of time-delay systems via Wirtinger-based double integral inequality

By Myeongjin Park, Oh-Min Kwon, Ju H. Park, Sangmoon Lee, E. Cha. at - Automatisierungstechnik, 2015

370 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/48373d7a0456b181e1e8285c677c260adb02131a

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In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay (2016, methodology): “However, compared with those in [23] and [6], the proof of Lemma 1 is very simple and straightforward in which an intermediate matrix is defined and the Schur complement is simply used only once.”
Recent developments on the stability of systems with aperiodic sampling: An overview (2017, methodology): “Finally, following the description given in Step 1, the application of the Wirtinger-based inequality to the case of triple integral-type of LKFs was considered in [212].”
Stabilization of Delay Systems: Delay-Dependent Impulsive Control (2017, background): “When there is no impulsive effect, some results for stability of system (17) have been derived, see ([6], [10], [26], [27].”
Further Improvement on Delay-Dependent Load Frequency Control of Power Systems via Truncated B–L Inequality (2018, background): “1] gives much tighter upper bounds on time derivative of triple integral terms than those derived by double Wirtinger-based integral inequality of Corollary 1 in [28] and double Jensen integral inequality of [13, Lemma 1], and the double integral inequality (26) of Lemma 5.”
Novel integral inequality approach on master–slave synchronization of chaotic delayed Lur’e systems with sampled-data feedback control (2016, background): “Besides, by using a double integral form of WBII in [51], we can take fully the relationship between ∫ t t−αh ∫ t θ ṙ T (s)R5ṙ(s)dsdθ , r(t), ∫ t t−αh r(s)ds and ∫ t t−αh ∫ t θ r(s)dsdθ , and ∫ t t−h ∫ t θ ṙ T (s)R6ṙ(s)dsdθ , r(t), ∫ t t−αh r(s)ds, ∫ t−αh t−h r(s)ds and ∫ t t−h ∫ t θ r(s)dsdθ into c”
Results on stability of linear systems with time varying delay (2017, methodology): “Compared with the simple functionals [1], augmented-based [5, 6, 9] and delay-partition-based functionals [13, 14] have been constructed to improve the stability criteria.”