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Alexandre Seuret - One of the best experts on this subject based on the ideXlab platform.

  • Comparison of bounding methods for stability analysis of systems with time-varying delays
    Journal of The Franklin Institute, 2017
    Co-Authors: Kun Liu, Alexandre Seuret
    Abstract:

    Integral inequalities for quadratic functions play an important role in the derivation of delay-dependent stability criteria for linear time-delay systems. Based on the Jensen Inequality , a reciprocally convex combination approach was introduced in [17] for deriving delay-dependent stability criterion, which achieves the same upper bound of the time-varying delay as the one on the use of the Moon et al.'s Inequality. Recently, a new Inequality called Wirtinger-based Inequality that encompasses the Jensen Inequality was proposed in [20] for the stability analysis of time-delay systems. In this paper, it is revealed that the reciprocally convex combination approach is effective only with the use of Jensen Inequality. When the Jensen Inequality is replaced by Wirtinger-based Inequality, the Moon et al.'s Inequality together with convex analysis can lead to less conservative stability conditions than the reciprocally convex combination Inequality. Moreover, we prove that the feasibility of an LMI condition derived by the Moon et al.'s Inequality as well as convex analysis implies the feasibility of an LMI condition induced by the reciprocally convex combination Inequality. Finally, the efficiency of the methods is demonstrated by some numerical examples, even though the corresponding system with zero-delay as well as the system without the delayed term are not stable.

  • stability of discrete time systems with time varying delays via a novel summation Inequality
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Alexandre Seuret, Frederic Gouaisbaut, Emilia Fridman
    Abstract:

    This technical note is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the technical note comes from the consideration of a new Inequality which is less conservative than the celebrated Jensen Inequality employed in the context of discrete-time delay systems. This Inequality is a discrete-time counterpart of the Wirtinger-based integral Inequality that was recently employed for the improved analysis of continuous-tine systems with delays. However, differently from the continuous-time case, the proof of the new Inequality is not based on the Wirtinger Inequality. The method is also combined with an efficient representation of the improved reciprocally convex combination Inequality in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

  • Stability of discrete-time systems with time-varying delays via a novel summation Inequality
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Alexandre Seuret, Frederic Gouaisbaut, Emilia Fridman
    Abstract:

    This paper is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the paper comes from the consideration of a new Inequality which is less conservative than the celebrated Jensen Inequality employed in the context of discrete-time delay systems. This Inequality is a discrete-time counterpart of the Wirtinger-based integral Inequality that was recently employed for the improved analysis of continuous-tine systems with delays. However, differently from the continuous-time case, the proof of the new Inequality is not based on the Wirtinger Inequality. The method is also combined with an efficient representation of the improved reciprocally convex combination Inequality in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

  • wirtinger based integral Inequality application to time delay systems
    Automatica, 2013
    Co-Authors: Alexandre Seuret, Frederic Gouaisbaut
    Abstract:

    In the last decade, the Jensen Inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities (LMIs). However, it is also well-known that this Inequality introduces an undesirable conservatism in the stability conditions and looking at the literature, reducing this gap is a relevant issue and always an open problem. In this paper, we propose an alternative Inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities. It is shown that this resulting Inequality encompasses the Jensen one and also leads to tractable LMI conditions. In order to illustrate the potential gain of employing this new Inequality with respect to the Jensen one, two applications on time-delay and sampled-data stability analysis are provided.

Poogyeon Park - One of the best experts on this subject based on the ideXlab platform.

  • auxiliary function based integral inequalities for quadratic functions and their applications to time delay systems
    Journal of The Franklin Institute-engineering and Applied Mathematics, 2015
    Co-Authors: Poogyeon Park, Won Il Lee, Seok Young Lee
    Abstract:

    Abstract Finding integral inequalities for quadratic functions plays a key role in the field of stability analysis. In such circumstances, the Jensen Inequality has become a powerful mathematical tool for stability analysis of time-delay systems. This paper suggests a new class of integral inequalities for quadratic functions via intermediate terms called auxiliary functions, which produce more tighter bounds than what the Jensen Inequality produces. To show the strength of the new inequalities, their applications to stability analysis for time-delay systems are given with numerical examples.

  • auxiliary function based summation inequalities for quadratic functions and their application to discrete time delay systems
    IFAC-PapersOnLine, 2015
    Co-Authors: Won Il Lee, Poogyeon Park, Seok Young Lee, R W Newcomb
    Abstract:

    Abstract Jensen Inequality has become a powerful tool of supporting summation inequalities for quadratic functions in order to obtain stability criteria for time-delayed systems since it achieves remarkable performance with a small number of decision variables. This paper suggests a new summation Inequality for quadratic functions based on an auxiliary function, which is superior to the Jensen Inequality. To demonstrate the superiority of the new Inequality, its application to stability analysis for discrete-time delay system is provided with a simple numerical example.

  • second order reciprocally convex approach to stability of systems with interval time varying delays
    Applied Mathematics and Computation, 2014
    Co-Authors: Poogyeon Park
    Abstract:

    Recently, some triple integral terms in the Lyapunov-Krasovskii functional have been introduced in the literature to reduce conservatism in the stability analysis of systems with interval time-varying delays. When we apply the Jensen Inequality to partitioned double integral terms in the derivation of LMI conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters emerges. This paper proposes an efficient method to manipulate such a combination by extending the lower bound lemma. Some numerical examples are given to demonstrate the improvement of the proposed method.

  • Improved criteria on robust stability and H ∞ performance for linear systems with interval time-varying delays via new triple integral functionals
    Applied Mathematics and Computation, 2014
    Co-Authors: Won Il Lee, Seok Young Lee, Poogyeon Park
    Abstract:

    This paper analyzes delay-dependent robust stability and H"~ performance of linear systems with an interval time-varying delay, based on a new Lyapunov-Krasovskii functional containing new triple integral terms. The time derivative of the Lyapunov-Krasovskii functional produces not only the strictly proper rational functions but also the non-strictly proper rational functions of the time-varying delays with first-order denominators. The combinations of the rational functions are directly handled via the Jensen Inequality lemma and the lower bound lemma for reciprocal convexity, whereas such combinations were approximated in the literature. The proposed criteria become less conservative with the significantly smaller number of decision variables than the existing criteria, which will be demonstrated by some numerical examples.

  • reciprocally convex approach to stability of systems with time varying delays
    Automatica, 2011
    Co-Authors: Poogyeon Park, Jeong Wan Ko, Changki Jeong
    Abstract:

    Whereas the upper bound lemma for matrix cross-product, introduced by Park (1999) and modified by Moon, Park, Kwon, and Lee (2001), plays a key role in guiding various delay-dependent criteria for delayed systems, the Jensen Inequality has become an alternative as a way of reducing the number of decision variables. It directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities, resulting in a linear combination of positive functions weighted by the inverses of convex parameters. This paper suggests the lower bound lemma for such a combination, which achieves performance behavior identical to approaches based on the integral Inequality lemma but with much less decision variables, comparable to those based on the Jensen Inequality lemma.

Frederic Gouaisbaut - One of the best experts on this subject based on the ideXlab platform.

  • stability of discrete time systems with time varying delays via a novel summation Inequality
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Alexandre Seuret, Frederic Gouaisbaut, Emilia Fridman
    Abstract:

    This technical note is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the technical note comes from the consideration of a new Inequality which is less conservative than the celebrated Jensen Inequality employed in the context of discrete-time delay systems. This Inequality is a discrete-time counterpart of the Wirtinger-based integral Inequality that was recently employed for the improved analysis of continuous-tine systems with delays. However, differently from the continuous-time case, the proof of the new Inequality is not based on the Wirtinger Inequality. The method is also combined with an efficient representation of the improved reciprocally convex combination Inequality in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

  • Stability of discrete-time systems with time-varying delays via a novel summation Inequality
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Alexandre Seuret, Frederic Gouaisbaut, Emilia Fridman
    Abstract:

    This paper is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the paper comes from the consideration of a new Inequality which is less conservative than the celebrated Jensen Inequality employed in the context of discrete-time delay systems. This Inequality is a discrete-time counterpart of the Wirtinger-based integral Inequality that was recently employed for the improved analysis of continuous-tine systems with delays. However, differently from the continuous-time case, the proof of the new Inequality is not based on the Wirtinger Inequality. The method is also combined with an efficient representation of the improved reciprocally convex combination Inequality in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

  • wirtinger based integral Inequality application to time delay systems
    Automatica, 2013
    Co-Authors: Alexandre Seuret, Frederic Gouaisbaut
    Abstract:

    In the last decade, the Jensen Inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities (LMIs). However, it is also well-known that this Inequality introduces an undesirable conservatism in the stability conditions and looking at the literature, reducing this gap is a relevant issue and always an open problem. In this paper, we propose an alternative Inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities. It is shown that this resulting Inequality encompasses the Jensen one and also leads to tractable LMI conditions. In order to illustrate the potential gain of employing this new Inequality with respect to the Jensen one, two applications on time-delay and sampled-data stability analysis are provided.

Emilia Fridman - One of the best experts on this subject based on the ideXlab platform.

  • stability of discrete time systems with time varying delays via a novel summation Inequality
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Alexandre Seuret, Frederic Gouaisbaut, Emilia Fridman
    Abstract:

    This technical note is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the technical note comes from the consideration of a new Inequality which is less conservative than the celebrated Jensen Inequality employed in the context of discrete-time delay systems. This Inequality is a discrete-time counterpart of the Wirtinger-based integral Inequality that was recently employed for the improved analysis of continuous-tine systems with delays. However, differently from the continuous-time case, the proof of the new Inequality is not based on the Wirtinger Inequality. The method is also combined with an efficient representation of the improved reciprocally convex combination Inequality in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

  • Stability of discrete-time systems with time-varying delays via a novel summation Inequality
    IEEE Transactions on Automatic Control, 2015
    Co-Authors: Alexandre Seuret, Frederic Gouaisbaut, Emilia Fridman
    Abstract:

    This paper is concerned with the stability analysis of discrete linear systems with time-varying delays. The novelty of the paper comes from the consideration of a new Inequality which is less conservative than the celebrated Jensen Inequality employed in the context of discrete-time delay systems. This Inequality is a discrete-time counterpart of the Wirtinger-based integral Inequality that was recently employed for the improved analysis of continuous-tine systems with delays. However, differently from the continuous-time case, the proof of the new Inequality is not based on the Wirtinger Inequality. The method is also combined with an efficient representation of the improved reciprocally convex combination Inequality in order to reduce the conservatism induced by the LMIs optimization setup. The effectiveness of the proposed result is illustrated by some classical examples from the literature.

Jun Cheng - One of the best experts on this subject based on the ideXlab platform.

  • a mismatched membership function approach to sampled data stabilization for t s fuzzy systems with time varying delayed signals
    Signal Processing, 2017
    Co-Authors: Bo Wang, Jun Cheng, Abdullah Albarakati, Habib M Fardoun
    Abstract:

    Abstract This paper is concerned with the issue of sampled-data stabilization for T-S fuzzy systems with time-varying delays, where the mismatched membership function (MMF) approach is proposed. The superiority of the proposed method lies that delay interval is split into flexible terminals, and newly Lyapunov–Krasovskii function (LKF) is constructed. By employing the Wirtinger Inequality and extended Jensen Inequality, some sufficient conditions of the sampled-data control for T-S fuzzy systems are established, which are efficiently solved by using standard available numerical packages. Finally, the superiority of achieved result is illustrated by the truck-trailer model.

  • robust delay probability distribution dependent stability of uncertain stochastic genetic regulatory networks with random discrete delays and distributed delays
    International Journal of Robust and Nonlinear Control, 2014
    Co-Authors: Wenqin Wang, Shouming Zhong, Jun Cheng
    Abstract:

    SUMMARY This study is concerned with the problem of robust delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with mixed time-varying delays. The parameter uncertainties are modeled as having a structured linear fractional form. Besides, we consider that the derivatives of the discrete time delays have different upper bounds in various delay intervals. Moreover, less conservative conditions are obtained by choosing an augmented novel Lyapunov–Krasovskii functional and using the lower bound lemma together with the Jensen Inequality lemma. Furthermore, the criteria can be applicable to both fast and slow time-varying delays. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.