An integral inequality in the stability problem of time-delay systems

By Keqin Gu. Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2000

1,627 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/5ba366ad15cb0c39adbcee98fd450725341cd780

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In Control and Systems Engineering

1. James Lam
2. Qing-Long Han
3. Shengyuan Xu
4. Yong He
5. Xianming Zhang
6. Min Wu
7. Frédéric Gouaisbaut
8. Peng Shi

Citations in the corpus

• A survey of linear matrix inequality techniques in stability analysis of delay systems (2008, background): “Lemma 3 (Jensen’s Inequality): (Gu 2000) For any constant matrix M2Rm m with M40, scalars b4a, PT2Aþ ATP2 þ Y1 þ YT1 þ Sþ hZ1 P1 PT2 þ ATP3 þ Y2 þ hZ2 PT2A1 YT1 þ ATP4 P1 P2 þ PT3Aþ YT2 þ hZT2 h Rþ Z3ð Þ PT3 P3 PT3A1 YT2 P4 AT1P2 Y1 þ PT4A AT1P3 Y2 PT4 AT1P4 þ PT4A1 S 2 64 3 755 0, ð22Þ R Y1 Y2 YT1…”
• Stabilization of linear systems with input delay and saturation—A parametric Lyapunov equation approach (2010, background): “Then xTy+ yTx xTPx+ yTP−1y Lemma 4 ([34]) For any positive-definite matrix M>0, two scalars 2 and 1 with 2 1, and a vector-valued function : [ 1, 2]→R such that the integrals in the following are well defined, then (∫ 2”
• Observer-Based Mixed H2/H∞ Control Design for Linear Systems with Time-Varying Delays: An LMI Approach (2008, methodology): “Among the past results on delay systems, the LMI approach is an efficient method to solve many filtering and control problems such as stability analysis and stabilization (see for instance the references [9-16]), H∞ filter design (see for instance the references [17-23]), H∞ control problems (see…”
• Delay-dependent stabilization of linear systems with time-varying state and input delays (2005, methodology): “2 in Gu et al. (2003)), we can conclude that (13) is asymptotically stable.”
• An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay (2017, background): “Various integral inequalities have been developed, such as Jensen inequality [7], Wirtinger-based inequality [3], auxiliary function based inequalities [8–10], Bessel-Legendre inequality [11], and free-matrix-based inequalities [12,13].”
• Overview of recent advances in stability of linear systems with time‐varying delays (2019, background): “In [45], Jensen integral inequality is introduced for the first time in the stability of time-delay systems.”
• Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling (2012, background): “Lemma 2: [11] For any constant matrix M ∈ Rm×m, M = M > 0, scalar p > 0, vector function x : [0, p] → R such that the integration in the sequel is well defined, the following holds”
• Consensus of multi‐agent systems with nonlinear dynamics and sampled‐data information: a delayed‐input approach (2013, neutral): “It follows from Jensen’s inequality [38] that”
• Jensen integral inequality approach to stability analysis of continuous-time systems with time-varying delay (2008, background): “This is due to their important role in many practical systems, and a great number of research results exist in the literature [1–16].”
• Brief paper New stability criteria for continuous-time systems with interval time-varying delay (2010, methodology): “Jensen’s integral inequality approach [6] is another important one.”