Hierarchy of LMI conditions for the stability analysis of time-delay systems

By Alexandre Seuret, Frédéric Gouaisbaut. Systems & control letters (Print), 2015

497 citations recorded by the source corpus.

Abstract Assessing stability of time-delay systems based on the Lyapunov–Krasovskii functionals has been the subject of many contributions. Most of the results are based, first, on an a priori design of functionals and, finally, on the use of the famous Jensen’s inequality. In contrast with this design process, the present paper aims at providing a generic set of integral inequalities which are asymptotically non conservative and then to design functionals driven by these inequalities. The resulting stability conditions form a hierarchy of LMI which is competitive with the most efficient existing methods (delay-partitioning, discretization and sum of squares), in terms of conservatism and of complexity. Finally, some examples show the efficiency of the method.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/af66991e6db0db36576a0a34f4f75a1de2d43470

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Citations in the corpus

An extended reciprocally convex matrix inequality for stability analysis of systems with time-varying delay (2017, background): “• What is more, matrix inequality (7) can be easily combined with the recently proposed integral/summation inequalities [10,11,27,28] to develop new inequalities with less estimation gaps.”
Networked control systems: a survey of trends and techniques (2020, background): “Borrowing the above idea, a two-sided looped functional is introduced in [36] in the”
Stability of Linear Systems With Time-Varying Delays Using Bessel–Legendre Inequalities (2018, methodology): “Following the results presented in [20] and [21] dealing with systems subject to constant discrete and distributed delays and also taking advantages of the Bessel–Legendre framework, the LMI conditions presented in Theorem 8 form a hierarchy.”
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”
Stability analysis of systems with time-varying delay via relaxed integral inequalities (2016, methodology): “In [25], a Bessel–Legendre inequality is proposed based on Legendre polynomials and Bessel inequality.”
Results on stability of linear systems with time varying delay (2017, background): “Very recently, based on the Legendre polynomials and Bessel inequality, a novel integral inequality, called Bessel– Legendre (B-L) inequality encompassing the Jensen's inequality and the Wirtinger-based integral, has been proposed [30].”
Two general integral inequalities and their applications to stability analysis for systems with time‐varying delay (2016, methodology): “Additionally, based on the Legendre polynomials and Bessel inequality, a novel integral inequality, called the Bessel–Legendre inequality, was developed in [22].”