Stability analysis of systems with time-varying delay via relaxed integral inequalities

By Chuan‐Ke Zhang, Yong He, Lin Jiang, Min Wu, Hongbing Zeng. Systems & control letters (Print), 2016

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Stability of Linear Systems With Time-Varying Delays Using Bessel–Legendre Inequalities (2018, background): “A list of technical tools that have been considered in the literature to solve this problem includes matrix inequalities [13], the reciprocally convex combination lemmas [16], [27].”
Overview of recent advances in stability of linear systems with time‐varying delays (2019, background): “Recently, an improved reciprocally convex inequality is proposed in [69] and developed in [70], which reads as”
An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay (2017, methodology): “• The inequalities in [24,25] can be directly obtained via the proposed matrix inequality (7).”
Stability analysis of linear systems with two additive time-varying delays via delay-product-type Lyapunov functional (2017, background): “In recent years, other integral inequalities, tighter than Wirtinger-based integral inequality, have been developed, for example, free-matrix-based inequality [27], auxiliary function-based inequalities [28, 29, 30, 31, 32, 33, 34], and Bessel-Legendre inequality [35], The further improved stability”
Asymmetric Lyapunov–Krasovskii functional method on stability of time‐delay systems (2021, unknown): “Given τ > 0, system (1) is asymptotically stable if there exist matrices P̃ = P̃, Q̃ = Q̃, and Z̃ > 0 such that [ P̃ + Z̃ −Z̃ ∗ τQ̃ + Z̃ ] > 0, (13)”