Wirtinger-based integral inequality: Application to time-delay systems

By Alexandre Seuret, Frédéric Gouaisbaut. at - Automatisierungstechnik, 2013

2,252 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/4a8ada0e562f6aaf6bd18397fb481e7a40538ef8

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In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Stability analysis of linear systems with two additive time-varying delays via delay-product-type Lyapunov functional (2017, background): “On the other hand, a tighter Wirtinger-based inequality was proposed in [23], while it has not been used for the systems with additive delays.”
Hierarchy of LMI conditions for the stability analysis of time-delay systems (2015, methodology): “The present paper aims at extending the results provided in [26, 27] by considering an alternative method based on the Bessel inequality and polynomial approximations.”
Resilient Event-Triggering $H_{\infty }$ Load Frequency Control for Multi-Area Power Systems With Energy-Limited DoS Attacks (2017, methodology): “By use of Wirtinger-based inequality [21] together with reciprocally convex approach [23] and the eventtriggered condition (7), we obtain”
Further improvement of Jensen inequality and application to stability of time-delayed systems (2016, background): “Recently, based on a Wirtinger inequality, Seuret and Gouaisbaut (2013) presented an analytically improved result that overcomes the Jensen inequality in (3) Vab(w) ≥ VJensen + 12 (b − a)3 ΩT1 (w)RΩ1(w) := VSeuret (5) whereΩ1(w) = b a (s − a+b 2 )w(s)ds, and its adoption significantly improves the…”
A Survey of Autonomous Underwater Vehicle Formation: Performance, Formation Control, and Communication Capability (2021, background): “We notice that many researchers contribute to how to calculate the delay upper bounds of delayed systems [188], [189], [190], [191].”
Event-Triggered Finite-Time Control for Networked Switched Linear Systems With Asynchronous Switching (2018, background): “Lemma 1 [32]: For any constant matrix M > 0, the following inequality holds for all continuously differentiable function ρ(·) in [a, b] → Rn”
Secondary delay‐partition approach on robust performance analysis for uncertain time‐varying Lurie nonlinear control system (2017, neutral): “ι=3 Ξι υ 1 2 1 X T υ 1 2 2 Y T υ 1 2 3 U T υ 1 2 4 W T ∗ −2R11 0 0 0 ∗ ∗ −2R12 0 0 ∗ ∗ ∗ −2R13 0 ∗ ∗ ∗ ∗ −2R14 ⎤⎥⎥⎥⎥⎦ < 0, (45) where Ξ̌2 = ⟨e1HReT21 + e2HGeT21⟩s.”
Finite-Time Event-Triggered Control for Semi-Markovian Switching Cyber-Physical Systems With FDI Attacks and Applications (2021, background): “…c 1 , c 2 > 0 and T f > 0 with c 1 c 2 , positive deﬁnite matrix R , system (7) is said to be stochastically ﬁnite-time stable related to ( c 1 , c 2 , R , Lemma 1: [51] For any given matrix χ > 0 and continuously Lemma 2: [52] Let ρ( t ) be a continuous function with 0 < ρ 1 ≤ ρ( t ) ≤ ρ 2 .”
Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay (2015, background): “This illustrates that the free-matrix-based integral inequality produces tighter bounds than the one in [23] does.”
Event-Triggered $H_\infty$ Load Frequency Control for Multiarea Power Systems Under Hybrid Cyber Attacks (2019, background): “Lemma 1 [49]: Consider a given matrix R = RT > 0.”
Survey on Recent Advances in Networked Control Systems (2016, neutral): “The input delay approach is to model the system (1) as the continuous-time system described by [34]{ ẋ(t) = Ax(t) +BKx(t− τ(t)), tk ≤ t < tk+1 x(θ) = x0 for θ = t0; 0 for θ < t0 (2) with a piecewise time-varying delay τ(t) := t− tk, tk ≤ t < tk+1 satisfying 0 ≤ τ(t) ≤ hu ∀t ≥ t0.”