Delay‐dependent stability and stabilization of neutral time‐delay systems

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Tutorial on Lyapunov-based methods for time-delay systems (2014, methodology): “This can be done by adding to V0 a triple integral term as suggested in [2,68] Vðxt ; _ xtÞ 1⁄4 V0ðxtÞþVZd ð _ xtÞ; VZd ð _ xtÞ 1⁄4 Z 0”
Novel delay‐derivative‐dependent stability criteria using new bounding techniques (2013, result): “There have been some delay-dependent stability criteria reported in the literature [3–9].”
Technical communique: Improved delay-range-dependent stability criteria for linear systems with time-varying delays (2010, neutral): “Such a Lyapunov functional type is very effective in the reduction of conservatism (Sun et al., 2009).”
Hierarchy of LMI conditions for the stability analysis of time-delay systems (2015, methodology): “The ﬁrst one proposed by [1, 8, 13, 28, 31, 30] is to consider a simpler structure for the LKF than the previously mentioned complete LKF which is applied to some higher dimensional comparison systems.”
Synchronization of an Inertial Neural Network With Time-Varying Delays and Its Application to Secure Communication (2018, background): “Lemma 2 (Schur Complement [37]): Given constant matrices 1, 2, and 3 with appropriate dimensions, where T1 = 1 and T2 = 2 > 0, then 1 + T3 −12 3 0 if and only if [ 1 T 3∗ − 2 ] 0, or [− 2 3 ∗ 1 ] 0.”