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Shouming Zhong - One of the best experts on this subject based on the ideXlab platform.
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improved delay dependent Stability Criteria for continuous system with two additive time varying delay components
Communications in Nonlinear Science and Numerical Simulation, 2014Co-Authors: Jun Cheng, Shouming Zhong, Hong Zhu, Yuping Zhang, Yong ZengAbstract:Abstract This paper investigated the problem of improved delay-dependent Stability Criteria for continuous system with two additive time-varying delay components. Free weighting matrices and convex combination method are not involved, which achieves much less numbers of linear matrix inequalities (LMIs) and LMIs scalar decision variables. By taking advantage of integral inequality and new Lyapunov–Krasovskii functional, new less conservative delay-dependent Stability criterion is derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
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novel delay dependent robust Stability Criteria for neutral systems with mixed time varying delays and nonlinear perturbations
Applied Mathematics and Computation, 2013Co-Authors: Jun Cheng, Hong Zhu, Shouming ZhongAbstract:This paper investigated the problem of delay-dependent robust Stability Criteria for neutral systems with mixed time-varying delays and nonlinear perturbations. A piecewise delay method is used in this paper, the variation interval of the time delay is divided into two subintervals by introducing its central point. Then, by employing the new Lyapunov-Krasovskii functional and linear matrix inequality technique, some new sufficient conditions are obtained. At last, numerical examples are provided to demonstrate the effectiveness of the obtained results.
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delay dependent Stability Criteria for genetic regulatory networks with time varying delays and nonlinear disturbance
Communications in Nonlinear Science and Numerical Simulation, 2012Co-Authors: Wenqin Wang, Shouming ZhongAbstract:Abstract This paper presents the robust Stability of genetic regulatory networks with time-varying delays and nonlinear disturbance. By choosing an appropriate new Lyapunov functional, a new delay-dependent Stability Criteria is obtained and formulated in terms of linear matrix inequalities (LMIs). The resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism. Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.
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improved delay dependent Stability Criteria for neural networks with two additive time varying delay components
Neurocomputing, 2012Co-Authors: Junkang Tian, Shouming ZhongAbstract:In this paper, the problem of Stability Criteria of neural networks with two additive time-varying delay components is investigated. Some new delay-dependent Stability Criteria are derived in terms of linear matrix inequalities by choosing a new class of Lyapunov functional. The obtained Criteria are less conservative because reciprocally convex approach and convex polyhedron approach are considered. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.
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Stability Criteria for impulsive reaction diffusion cohen grossberg neural networks with time varying delays
Mathematical and Computer Modelling, 2010Co-Authors: Shouming ZhongAbstract:This paper studies impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays and Neumann boundary conditions. By employing the topological degree theory, delay differential inequality with impulses, linear matrix inequality (LMI) and Poincare inequality, a set of sufficient conditions are derived to ensure the existence, uniqueness and global exponential Stability of the equilibrium point. These global exponential Stability conditions depend on the reaction-diffusion term. A comparison between our results and the previous results shows that our results establish a new set of Stability Criteria for reaction-diffusion neural networks and have improved the previous results.
Peng Shi - One of the best experts on this subject based on the ideXlab platform.
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novel robust Stability Criteria for stochastic hopfield neural networks with time delays
Systems Man and Cybernetics, 2009Co-Authors: Rongni Yang, Huijun Gao, Peng ShiAbstract:In this paper, the problem of asymptotic Stability for stochastic Hopfield neural networks (HNNs) with time delays is investigated. New delay-dependent Stability Criteria are presented by constructing a novel Lyapunov-Krasovskii functional. Moreover, the results are further extended to the delayed stochastic HNNs with parameter uncertainties. The main idea is based on the delay partitioning technique, which differs greatly from most existing results and reduces conservatism. Numerical examples are provided to illustrate the effectiveness and less conservativeness of the developed techniques.
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robust Stability Criteria for uncertain neutral system with time delay and nonlinear uncertainties
Chaos Solitons & Fractals, 2008Co-Authors: Jinhui Zhang, Peng Shi, Jiqing QiuAbstract:Abstract The problem of robust Stability for a class of uncertain neutral system with time-varying delay and nonlinear uncertainties is studied in this paper. A new delay-dependent Stability Criteria is presented by using Lyapunov method. The Criteria is given in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in Matlab. A numerical example is given to illustrate the effectiveness of the developed techniques.
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novel robust Stability Criteria for uncertain stochastic hopfield neural networks with time varying delays
Nonlinear Analysis-real World Applications, 2007Co-Authors: Jinhui Zhang, Peng Shi, Jiqing QiuAbstract:The problem of stochastic robust Stability of a class of stochastic Hopfield neural networks with time-varying delays and parameter uncertainties is investigated in this paper. The parameter uncertainties are time-varying and norm-bounded. The time-delay factors are unknown and time-varying with known bounds. Based on Lyapunov–Krasovskii functional and stochastic analysis approaches, some new Stability Criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be robustly stochastically asymptotically stable in the mean square for all admissible uncertainties. Numerical examples are given to illustrate the effectiveness and less conservativeness of the developed techniques.
Qinglong Han - One of the best experts on this subject based on the ideXlab platform.
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novel Stability Criteria for linear time delay systems using lyapunov krasovskii functionals with a cubic polynomial on time varying delay
IEEE CAA Journal of Automatica Sinica, 2021Co-Authors: Xianming Zhang, Qinglong HanAbstract:One of challenging issues on Stability analysis of time-delay systems is how to obtain a Stability criterion from a matrix-valued polynomial on a time-varying delay. The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval. The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer. The second contribution of this paper is to introduce a novel Lyapunov-Krasovskii functional, which includes a cubic polynomial on a time-varying delay, in Stability analysis of time-delay systems. Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities, two Stability Criteria are derived for two cases of the time-varying delay. A well-studied numerical example is given to show that the proposed Stability Criteria are of less conservativeness than some existing ones.
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hierarchical type Stability Criteria for delayed neural networks via canonical bessel legendre inequalities
IEEE Transactions on Systems Man and Cybernetics, 2018Co-Authors: Xianming Zhang, Qinglong Han, Zhigang ZengAbstract:This paper is concerned with global asymptotic Stability of delayed neural networks. Notice that a Bessel–Legendre inequality plays a key role in deriving less conservative Stability Criteria for delayed neural networks. However, this inequality is in the form of Legendre polynomials and the integral interval is fixed on ${[{-}h,0]}$ . As a result, the application scope of the Bessel–Legendre inequality is limited. This paper aims to develop the Bessel–Legendre inequality method so that less conservative Stability Criteria are expected. First, by introducing a canonical orthogonal polynomial sequel, a canonical Bessel–Legendre inequality and its affine version are established, which are not explicitly in the form of Legendre polynomials. Moreover, the integral interval is shifted to a general one $ {[a,b]}$ . Second, by introducing a proper augmented Lyapunov–Krasovskii functional, which is tailored for the canonical Bessel–Legendre inequality, some sufficient conditions on global asymptotic Stability are formulated for neural networks with constant delays and neural networks with time-varying delays, respectively. These conditions are proven to have a hierarchical feature: the higher level of hierarchy, the less conservatism of the Stability criterion. Finally, three numerical examples are given to illustrate the efficiency of the proposed Stability Criteria.
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novel delay derivative dependent Stability Criteria using new bounding techniques
International Journal of Robust and Nonlinear Control, 2013Co-Authors: Xianming Zhang, Qinglong HanAbstract:SUMMARY This paper studies the Stability of linear systems with interval time-varying delays. By constructing a new Lyapunov–Krasovskii functional, two delay-derivative-dependent Stability Criteria are formulated by incorporating with two different bounding techniques to estimate some integral terms appearing in the derivative of the Lyapunov–Krasovskii functional. The first Stability criterion is derived by using a generalized integral inequality, and the second Stability criterion is obtained by employing a reciprocally convex approach. When applying these two Stability Criteria to check the Stability of a linear system with an interval time-varying delay, it is shown through some numerical examples that the first Stability criterion can provide a larger upper bound of the time-varying delay than the second Stability criterion. Copyright © 2012 John Wiley & Sons, Ltd.
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technical communique improved Stability Criteria and controller design for linear neutral systems
Automatica, 2009Co-Authors: Qinglong HanAbstract:This paper is concerned with the problems of Stability and H"~ control of linear neutral systems. Firstly, some new simple Lyapunov-Krasovskii functionals are constructed by uniformly dividing the discrete delay interval into multiple segments, and choosing proper functionals with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functionals. Then using these new simple Lyapunov-Krasovskii functionals, some new delay-dependent Stability Criteria are derived. These Criteria include some existing results as their special cases and are much less conservative than some existing results, which is shown through a numerical example. Secondly, a delay-dependent bounded real lemma (BRL) is established. Employing the obtained BRL, some delay-dependent sufficient conditions for the existence of a delayed state feedback controller, which ensure asymptotic Stability and a prescribed H"~ performance level of the corresponding closed-loop system, is formulated in terms of a linear matrix inequality (LMI). A numerical example is also given to illustrate the effectiveness of the design method.
Jiqing Qiu - One of the best experts on this subject based on the ideXlab platform.
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robust Stability Criteria for uncertain neutral system with time delay and nonlinear uncertainties
Chaos Solitons & Fractals, 2008Co-Authors: Jinhui Zhang, Peng Shi, Jiqing QiuAbstract:Abstract The problem of robust Stability for a class of uncertain neutral system with time-varying delay and nonlinear uncertainties is studied in this paper. A new delay-dependent Stability Criteria is presented by using Lyapunov method. The Criteria is given in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in Matlab. A numerical example is given to illustrate the effectiveness of the developed techniques.
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novel robust Stability Criteria for uncertain stochastic hopfield neural networks with time varying delays
Nonlinear Analysis-real World Applications, 2007Co-Authors: Jinhui Zhang, Peng Shi, Jiqing QiuAbstract:The problem of stochastic robust Stability of a class of stochastic Hopfield neural networks with time-varying delays and parameter uncertainties is investigated in this paper. The parameter uncertainties are time-varying and norm-bounded. The time-delay factors are unknown and time-varying with known bounds. Based on Lyapunov–Krasovskii functional and stochastic analysis approaches, some new Stability Criteria are presented in terms of linear matrix inequalities (LMIs) to guarantee the delayed neural network to be robustly stochastically asymptotically stable in the mean square for all admissible uncertainties. Numerical examples are given to illustrate the effectiveness and less conservativeness of the developed techniques.
Russell Frith - One of the best experts on this subject based on the ideXlab platform.
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an assessment of coal pillar system Stability Criteria based on a mechanistic evaluation of the interaction between coal pillars and the overburden
International journal of mining science and technology, 2017Co-Authors: Guy Reed, Kent Mctyer, Russell FrithAbstract:Abstract Coal pillar design has historically assigned a factor of safety (FoS) or Stability factor (SF) according to their estimated strength and the assumed overburden load acting on them. Acceptable FoS values have been assigned based on past mining experience or a statistical link between FoS and probability of failure (PoF). Pillar width-to-height (w/h) ratio has long been established as having a material influence on both pillar strength and its potential failure mode. However, there has been significant disagreement on using both factor of safety (FoS) and w/h as part of pillar system Stability criterion, as compared to using FoS in isolation. This paper will argue that there are valid technical reasons to bring w/h ratio into system Stability Criteria (other than its influence on pillar strength), as it is related to the post-failure stiffness of the pillar, as measured in situ, and its interaction with overburden stiffness. When overburden stiffness is also brought into pillar system Stability considerations, two issues emerge. The first is the width-to-depth (W/D) ratio of the panel and whether it is sub-critical or super-critical from a surface subsidence perspective. The second relates to a re-evaluation of pillar FoS based on whether the pillar is in an elastic or non-elastic (i.e., post-yield) state in its as-designed condition, as this is relevant to maintaining overburden stiffness at the highest possible level. The significance of the model is the potential to maximise both reserve recovery and mining efficiencies without any discernible increase in geotechnical risk, particularly in thick seams and higher depth of cover mining situations. At a time when mining economics are, at best, marginal, removing potentially unnecessary design conservatism is of interest to all mine operators and is an important topic for discussion amongst the geotechnical community.
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An assessment of coal pillar system Stability Criteria based on a mechanistic evaluation of the interaction between coal pillars and the overburden
Elsevier, 2017Co-Authors: Guy Reed, Kent Mctyer, Russell FrithAbstract:Coal pillar design has historically assigned a factor of safety (FoS) or Stability factor (SF) according to their estimated strength and the assumed overburden load acting on them. Acceptable FoS values have been assigned based on past mining experience or a statistical link between FoS and probability of failure (PoF). Pillar width-to-height (w/h) ratio has long been established as having a material influence on both pillar strength and its potential failure mode. However, there has been significant disagreement on using both factor of safety (FoS) and w/h as part of pillar system Stability criterion, as compared to using FoS in isolation. This paper will argue that there are valid technical reasons to bring w/h ratio into system Stability Criteria (other than its influence on pillar strength), as it is related to the post-failure stiffness of the pillar, as measured in situ, and its interaction with overburden stiffness. When overburden stiffness is also brought into pillar system Stability considerations, two issues emerge. The first is the width-to-depth (W/D) ratio of the panel and whether it is sub-critical or super-critical from a surface subsidence perspective. The second relates to a re-evaluation of pillar FoS based on whether the pillar is in an elastic or non-elastic (i.e., post-yield) state in its as-designed condition, as this is relevant to maintaining overburden stiffness at the highest possible level. The significance of the model is the potential to maximise both reserve recovery and mining efficiencies without any discernible increase in geotechnical risk, particularly in thick seams and higher depth of cover mining situations. At a time when mining economics are, at best, marginal, removing potentially unnecessary design conservatism is of interest to all mine operators and is an important topic for discussion amongst the geotechnical community. Keywords: Coal pillars, Stability, Overburden, Post-failure behaviour, Stability criteri
