Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay

By Hongbing Zeng, Yong He, Min Wu, Jinhua She. IEEE Transactions on Automatic Control, 2015

756 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/364fb6732fe52c6192c9107dfe7b95e29446cb3f

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Citations in the corpus

Stability analysis of systems with time-varying delay via relaxed integral inequalities (2016, methodology): “• Compared with the criteria obtained by different inequalities (Jensen inequality [27], Wirtinger-based inequality [9], freematrix-based inequality [18]), the new type of LKF [8], and the augmented systemmodel [41], the proposed Theorem 2.”
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.”
Asymmetric Lyapunov–Krasovskii functional method on stability of time‐delay systems (2021, background): “By Lemma 1, according to (10) and (4), for (6) we deduce”
Overview of recent advances in stability of linear systems with time‐varying delays (2019, methodology): “The affine versions of (32) and (33) can be found in [67, 97] or [98].”
Results on stability of linear systems with time varying delay (2017, background): “Based on the above discussions, a new integral inequality is developed, which covers Wintinger-based integral inequality [22] and free matrix-based integral inequality [28] as special cases.”
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”
New results on stability analysis for systems with discrete distributed delay (2015, methodology): “Unlike the method in Zeng et al. (2015) , Theorem 3 takes information on the double integral of the system state into consideration, which helps to reduce the conservatism.”