Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems

By PooGyeon Park, Won Il Lee, Seok Young Lee. Journal of the Franklin Institute, 2015

807 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/829397e0960bf0cf5da057577076d0a52a8c5943

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In Control and Systems Engineering

Citations in the corpus

Stability of Linear Systems With Time-Varying Delays Using Bessel–Legendre Inequalities (2018, methodology): “Remark 2: The previous inequality includes Jensen’s inequality [7], the Wirtinger-based integral inequality and the auxiliary-function based integral inequality [17] as particular cases when N = 0, 1, 2, respectively.”
Stability analysis of systems with time-varying delay via relaxed integral inequalities (2016, methodology): “By setting λ1(s, a, b) = 2s−b−a b−a , the following equations can be obtained via simple calculations [18,24]:  b”
Overview of recent advances in stability of linear systems with time‐varying delays (2019, background): “It should be pointed that stability of the system (1) with unknown information on the derivative of h(t) is also investigated in [53] using the auxiliary-function-based integral inequality (33), but those vectors induced from (33) do not exist in the derivative of the chosen Lyapunov–Krasovskii func”
Recent developments on the stability of systems with aperiodic sampling: An overview (2017, background): “Further reﬁnements were developed in [145], where the authors considered a discretized version of this inequality, in [273], where additional free-weighted matrices are introduced or in [214] using auxiliary functions.”
Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay (2016, background): “1 [23] are all special cases of the two general ones developed in Lemma 1.”
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”
An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay (2017, result): “Theorem 8 achieves the reduction of both the conservatism and the NoVs in comparison with the auxiliary-function-based inequality (Hien & Trinh, 2015; Park et al., 2015).”