Delay-dependent criterion for exponential stability analysis of neural networks with time-varying delays

This note investigates the problem of exponential stability of neural networks with time-varying delays. To derive a less conservative stability condition, a novel augmented Lyapunov-Krasovskii functional (LKF) which includes triple and quadruple-integral terms is employed. In order to reduce the complexity of the stability test, the convex combination method is utilized to derive an improved delay dependent stability criterion in the form of linear matrix inequalities (LMIs). The superiority of the proposed approach is demonstrated by two comparative examples

On Computing the Worst-case H∞ Performance of Lur'e Systems with Uncertain Time-invariant Delays

This paper presents a worst-case H∞ performance analysis for Lur'e systems with time-invariant delays. The sucient condition to guarantee an upper bound of worst-case performance is developed based on the delay-partitioning Lyapunov-Krasovskii functional containing the integral of sector-bounded nonlinearities. Using Jensen inequality and S-procedure, the delay-dependent criterion is given in terms of linear matrix inequalities. In addition, we extend the criterion to compute the worst-case performance for Lur'e systems subject to norm-bounded uncertainties by using a matrix eliminating lemma. Numerical results show that our criterion provide the least upper bound on the worst-case H∞ performance comparing to the criteria derived based on existing techniques

Stability Analysis of Delayed Genetic Regulatory Networks via a Relaxed Double Integral Inequality

Time delay arising in a genetic regulatory network may cause the instability. This paper is concerned with the stability analysis of genetic regulatory networks with interval time-varying delays. Firstly, a relaxed double integral inequality, named as Wirtinger-type double integral inequality (WTDII), is established to estimate the double integral term appearing in the derivative of Lyapunov-Krasovskii functional with a triple integral term. And it is proved theoretically that the proposed WTDII is tighter than the widely used Jensen-based double inequality and the recently developed Wiringter-based double inequality. Then, by applying the WTDII to the stability analysis of a delayed genetic regulatory network, together with the usage of useful information of regulatory functions, several delay-range- and delay-rate-dependent (or delay-rate-independent) criteria are derived in terms of linear matrix inequalities. Finally, an example is carried out to verify the effectiveness of the proposed method and also to show the advantages of the established stability criteria through the comparison with some literature

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the U.K. under Grants BB/C506264/1 and 100/EGM17735, an International Joint Project sponsored by the Royal Society of the U.K., the Research Grants Council of Hong Kong under Grant HKU 7031/06P, the National Natural Science Foundation of China under Grant 60804028, and the Alexander von Humboldt Foundation of Germany

An improved stability criterion for discrete-time time-delayed Lur’e systemwith sector-bounded nonlinearities

The absolute stability problem of discrete-time time-delayed Lur\u27e systems with sector bounded nonlinearities is investigated in this paper. Firstly, a modified Lyapunov-Krasovskii functional (LKF) is designed with augmenting additional double summation terms, which complements more coupling information between the delay intervals and other system state variables than some previous LKFs. Secondly, some improved delay-dependent absolute stability criteria based on linear matrix inequality form (LMI) are proposed via the modified LKF and the relaxed free-matrix-based summation inequality technique application. The stability criteria are less conservative than some results previously proposed. The reduction of the conservatism mainly relies on the full use of the relaxed summation inequality technique based on the modified LKF. Finally, two common numerical examples are presented to show the effectiveness of the proposed approach

A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems

This is an Author's Accepted Manuscript of an article published in Antonio González (2021) A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems, International Journal of Systems Science, 52:8, 1707-1718, DOI: 10.1080/00207721.2020.1869344, available online at: http://www.tandfonline.com/10.1080/00207721.2020.1869344[EN] This paper investigates the exponential stability of uncertain time delay systems using a novel descriptor redundancy approach based on delay partitioning. First, the original system is casted into an equivalent descriptor singular state¿space representation by introducing redundant state variables so that the resulting delay is progressively reduced. From the equivalent model and applying Lyapunov Functional method, a sufficient condition based on Linear Matrix Inequalities (LMIs) for exponential stability with guaranteed decay rate performance is obtained. As a result, the inherent conservatism of Lyapunov¿Krasovskii functional techniques can arbitrarily be reduced by increasing the number of delay partition intervals including decay rate performance and model uncertainties in polytopic form. Various benchmark examples are provided to validate the effectiveness of the proposed method, showing better trade-off between conservatism and performance in comparison to previous approaches.This work was supported by project PGC2018-098719-B-I00 (MCIU/AEI/FEDER,UE).González Sorribes, A. (2021). A novel descriptor redundancy method based on delay partition for exponential stability of time delay systems. International Journal of Systems Science. 52(8):1707-1718. https://doi.org/10.1080/00207721.2020.18693441707171852

New summation inequalities and their applications to discrete-time delay systems

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by establishing less conservative stability conditions for a class of linear discrete-time systems with an interval time-varying delay in the framework of linear matrix inequalities. The effectiveness and least conservativeness of the derived stability conditions are shown by academic and practical examples.Comment: 15 pages, 01 figur

Further results on exponential estimates of markovian jump systems with mode-dependent time-varying delays

This technical note studies the problem of exponential estimates for Markovian jump systems with mode-dependent interval time-varying delays. A novel LyapunovKrasovskii functional (LKF) is constructed with the idea of delay partitioning, and a less conservative exponential estimate criterion is obtained based on the new LKF. Illustrative examples are provided to show the effectiveness of the proposed results. © 2010 IEEE.published_or_final_versio