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Pierdomenico Pepe - One of the best experts on this subject based on the ideXlab platform.
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a relaxed lyapunov Krasovskii condition for global exponential stability of lipschitz time delay systems
Conference on Decision and Control, 2019Co-Authors: Antoine Chaillet, Jakub Orlowski, Pierdomenico PepeAbstract:For nonlinear time-delay systems with globally Lipschitz vector fields, we propose a relaxed sufficient condition for global exponential stability (GES), in which the dissipation rate of the Lyapunov-Krasovskii functional is not needed to involve the functional itself, but merely the point-wise current value of the solution. Our proof technique consists in explicitly constructing a Lyapunov-Krasovskii functional that satisfies existing criteria for GES. Consequences for robustness to exogenous inputs are briefly evoked and an example taken from neuroscience literature illustrates the applicability of the result.
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Integral input-to-state stability of delay systems based on Lyapunov-Krasovskii functionals with point-wise dissipation rate
2018Co-Authors: Antoine Chaillet, Pierdomenico PepeAbstract:We show that a Lyapunov-Krasovskii functional whose dissipation rate involves solely the current instantaneous value of the state norm is enough to guarantee integral inputto-state stability (iISS). This result generalizes existing sufficient conditions for iISS, where the dissipation rate involves the whole Lyapunov-Krasovskii functional itself, and simplifies their applicability. Moreover, it provides a more natural bridge with the classical condition for global asymptotic stability of input-free systems. The proof strategy we employ relies on a novel characterization of global asymptotic stability, which may be of interest on its own.
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lyapunov Krasovskii characterization of the input to state stability for neutral systems in hale s form
Systems & Control Letters, 2017Co-Authors: Pierdomenico Pepe, Iasson Karafyllis, Zhongping JiangAbstract:Abstract The primary contribution of the paper is to show that the Lyapunov–Krasovskii conditions available in the literature, for checking the input-to-state stability property of systems described by neutral functional differential equations in Hale’s form, are also necessary. It is shown that the Lyapunov–Krasovskii conditions available in the literature are equivalent to the input-to-state stability property, for an enlarged class of neutral systems. Finally, a novel necessary and sufficient condition for the input-to-state stability property is provided.
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stabilization of retarded systems of neutral type by control lyapunov Krasovskii functionals
Systems & Control Letters, 2016Co-Authors: Pierdomenico PepeAbstract:Abstract This paper deals with the stabilization and the practical stabilization of nonlinear systems described by neutral functional differential equations in Hale’s form, affine in the control input. Artstein’s methodology and Sontag’s universal formula are investigated for this class of systems, by means of invariantly differentiable control Lyapunov–Krasovskii functionals.
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a small gain condition for iiss of interconnected retarded systems based on lyapunov Krasovskii functionals
Automatica, 2010Co-Authors: Hiroshi Ito, Pierdomenico Pepe, Zhongping JiangAbstract:This paper considers interconnected retarded nonlinear systems. Integral input-to-state stable subsystems and the construction of Lyapunov-Krasovskii functionals for their interconnections are focused on. Both discrete and distributed time-delays in the subsystems and the communication channels are covered. This paper provides a sufficient small-gain type condition for the stability of the interconnected systems with respect to external inputs in the framework of Lyapunov-Krasovskii functionals. Global asymptotic stability is addressed as a special case which deals with time-varying delays in communication channels effectively.
Bin Zhou - One of the best experts on this subject based on the ideXlab platform.
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improved razumikhin and Krasovskii approaches for discrete time time varying time delay systems
Automatica, 2018Co-Authors: Bin ZhouAbstract:Abstract This paper studies stability of discrete-time time-varying time-delay systems. The existing Razumikhin and Krasovskii stability approaches for this class of systems are improved in the sense that the time-shifts of the Razumikhin functions and Krasovskii functionals are allowed to take both negative and positive values. Three kinds of stability concepts, say, uniform stability, uniformly asymptotic stability and uniformly exponential stability, are considered. The improvements of the Razumikhin and Krasovskii approaches are achieved by using the concept of uniformly asymptotically stable (UAS) function, the notion of overshoot associated with the UAS function and an improved comparison lemma. Both delay-dependent and delay-independent stability theorems are obtained for a class of discrete-time linear time-delay systems by using the improved Razumikhin and Krasovskii stability approaches. Numerical examples demonstrate the effectiveness of the proposed methods.
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improved razumikhin and Krasovskii stability criteria for time varying stochastic time delay systems
Automatica, 2018Co-Authors: Bin Zhou, Weiwei LuoAbstract:The problem of pth moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii stability approaches. Both pth moment asymptotic stability and (integral) input-to-state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison lemmas. The established results show that time-derivatives of the constructed Razumikhin functions and Krasovskii functionals are allowed to be indefinite, which improve the existing results on this topic. By applying the obtained results for stochastic systems, we also analyze briefly the stability of time-varying deterministic time-delay systems. Finally, examples are provided to illustrate the effectiveness of the proposed results.
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razumikhin and Krasovskii stability theorems for time varying time delay systems
Automatica, 2016Co-Authors: Bin Zhou, Alexey V EgorovAbstract:The main results of the paper are generalizations of the Razumikhin and of the Krasovskii classical stability theorems for stability analysis of time-varying time-delay systems. The condition of negativity of the time-derivative of Razumikhin functions and Krasovskii functionals is weakened. This is achieved by using the notion and properties of uniformly stable functions. We also show how to apply the results to the stability analysis of linear time-varying time-delay systems of retarded type. Both the system matrices and time-delays are allowed to be time-varying. Some constructive sufficient stability conditions are obtained and their effectiveness is demonstrated by some examples.
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improved razumikhin and Krasovskii stability criteria for time varying stochastic time delay systems
arXiv: Dynamical Systems, 2016Co-Authors: Bin Zhou, Weiwei LuoAbstract:The problem of p-th moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii stability theorems. Both p-th moment asymptotic stability and (integral) input-to-state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison principles. The established results show that time-derivatives of the constructed Razumikhin functions and Krasovskii functionals are allowed to be indefinite, which improve the existing results on this topic. By applying the obtained results for stochastic systems, we also analyze briefly the stability of time-varying deterministic time-delay systems. Finally, examples are provided to illustrate the effectiveness of the proposed results.
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lyapunov Krasovskii functionals for predictor feedback control of linear systems with multiple input delays
Chinese Control Conference, 2014Co-Authors: Bin Zhou, James LamAbstract:Abstract This paper is concerned with the Lyapunov–Krasovskii functional construction of linear control systems with multiple input delays. By transforming the predictor feedback control systems into a delay-free linear system with external inputs, a Lyapunov–Krasovskii functional is constructed in terms of a set of linear matrix inequalities (LMIs). It is shown that the solvability of this set of LMIs is equivalent to the asymptotic stability of the delay-free linear system induced from the predictor feedback control system. The proposed Lyapunov–Krasovskii functional is also found to be an ISS Lyapunov–Krasovskii functional for the predictor feedback control systems. An example is worked out to validate the effectiveness of the proposed method.
Zhongping Jiang - One of the best experts on this subject based on the ideXlab platform.
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lyapunov Krasovskii characterization of the input to state stability for neutral systems in hale s form
Systems & Control Letters, 2017Co-Authors: Pierdomenico Pepe, Iasson Karafyllis, Zhongping JiangAbstract:Abstract The primary contribution of the paper is to show that the Lyapunov–Krasovskii conditions available in the literature, for checking the input-to-state stability property of systems described by neutral functional differential equations in Hale’s form, are also necessary. It is shown that the Lyapunov–Krasovskii conditions available in the literature are equivalent to the input-to-state stability property, for an enlarged class of neutral systems. Finally, a novel necessary and sufficient condition for the input-to-state stability property is provided.
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a small gain condition for iiss of interconnected retarded systems based on lyapunov Krasovskii functionals
Automatica, 2010Co-Authors: Hiroshi Ito, Pierdomenico Pepe, Zhongping JiangAbstract:This paper considers interconnected retarded nonlinear systems. Integral input-to-state stable subsystems and the construction of Lyapunov-Krasovskii functionals for their interconnections are focused on. Both discrete and distributed time-delays in the subsystems and the communication channels are covered. This paper provides a sufficient small-gain type condition for the stability of the interconnected systems with respect to external inputs in the framework of Lyapunov-Krasovskii functionals. Global asymptotic stability is addressed as a special case which deals with time-varying delays in communication channels effectively.
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construction of lyapunov Krasovskii functionals for interconnection of retarded dynamic and static systems via a small gain condition
Conference on Decision and Control, 2009Co-Authors: Hiroshi Ito, Pierdomenico Pepe, Zhongping JiangAbstract:This paper addresses the problem of constructing Lyapunov-Krasovskii functionals for verifying integral input-to-state stability(iISS) and input-to-state stability(ISS) of time-delay nonlinear systems. Based on decomposition of a time-delay system into a dynamic component (a functional differential equation) and static components (functional algebraic equations), this paper develops an iISS small-gain theorem for the interconnection of these components to assess the stability of the overall time-delay system. Both discrete and distributed delays can be involved in the dynamic and the static components. The result can be considered as a counterpart of the author's previous work which only deals with dynamic components. For the construction of Lyapunov-Krasovskii functionals, this paper introduces a new technique which differs from the one employed in the dynamic case.
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further results on lyapunov Krasovskii functionals via nonlinear small gain conditions for interconnected retarded iiss systems
American Control Conference, 2009Co-Authors: Hiroshi Ito, Pierdomenico Pepe, Zhongping JiangAbstract:This paper presents further results on the problem of establishing stability of retarded nonlinear interconnected systems comprising integral input-to-state stable subsystems. It is shown that the stability of the interconnected systems with respect to external signals can be verified by constructing Lyapunov-Krasovskii functionals explicitly whenever small-gain type conditions are satisfied. The primary result [12] is generalized in two aspects. One is to introduce a new flexibility in constructing Lyapunov-Krasovskii functionals to deal with distributed delays more effectively. The other is to cover systems involving time-varying delays in interconnecting channels.
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a small gain condition for integral input to state stability of interconnected retarded nonlinear systems
Conference on Decision and Control, 2008Co-Authors: Hiroshi Ito, Pierdomenico Pepe, Zhongping JiangAbstract:In this paper, interconnected retarded nonlinear systems are considered. Both the constant discrete and distributed time-delays in the subsystems and the interconnections are addressed. A sufficient small-gain type condition for integral input-to-state stability with respect to external inputs is provided in the framework of Lyapunov-Krasovskii functionals.
Vladimir L Kharitonov - One of the best experts on this subject based on the ideXlab platform.
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lyapunov Krasovskii functionals for scalar neutral type time delay equations
Systems & Control Letters, 2009Co-Authors: Juan Eduardo Velazquezvelazquez, Vladimir L KharitonovAbstract:Abstract In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar neutral type time delay equation is considered. The construction of the functionals depends on the so-called Lyapunov functions which satisfy a delay equation with additional boundary conditions. It is shown that these functionals admit lower and upper quadratic bounds. Exponential estimates for solutions of the scalar neutral type time delay equations based on the Lyapunov–Krasovskii functionals are presented. A new definition of the Lyapunov function is given, and a detailed analysis of its properties is carried out.
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complete type lyapunov Krasovskii functionals with a given cross term in the time derivative
Conference on Decision and Control, 2005Co-Authors: Sabine Mondie, Vladimir L Kharitonov, Omar SantosAbstract:A general expression for the complete type quadratic Lyapunov-Krasovskii functional with a given cross term in the time derivative is presented. Some robust stability conditions and exponential estimates are obtained.
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robust stability of neutral systems a lyapunov Krasovskii constructive approach
International Journal of Robust and Nonlinear Control, 2004Co-Authors: S A Rodriguez, Vladimir L Kharitonov, J M Dion, Luc DugardAbstract:In this paper, robust stability of uncertain linear neutral systems is analysed via a Lyapunov–Krasovskii constructive approach. This paper is the first attempt to compute the Lyapunov–Krasovskii functional for a given time derivative functional w(·) for the class of linear neutral type time delay systems. Copyright © 2004 John Wiley & Sons, Ltd.
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lyapunov Krasovskii functionals for scalar time delay equations
Systems & Control Letters, 2004Co-Authors: Vladimir L KharitonovAbstract:Abstract In this paper a procedure for construction of complete type Lyapunov–Krasovskii functionals for a scalar time delay equation is considered. The functionals depend on a scalar function which satisfies a time delay equation. It is shown that the scalar function satisfies also a high order delay free differential equation. In order to specify the function additional boundary conditions are given. Robust stability conditions based on the Lyapunov–Krasovskii functionals are presented.
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lyapunov Krasovskii functionals for additional dynamics
International Journal of Robust and Nonlinear Control, 2003Co-Authors: Vladimir L Kharitonov, Daniel MelchoraguilarAbstract:A class of Lyapunov–Krasovskii functionals for the additional dynamics introduced by special transformation of time delay systems is given in the paper. Some basic properties of the functionals are also discussed. Copyright © 2003 John Wiley & Sons, Ltd.
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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Overview of recent advances in stability of linear systems with time-varying delays
IET Control Theory and Applications, 2019Co-Authors: Xianming Zhang, Qinglong Han, Alexandre Seuret, Frédéric GouaisbautAbstract:This study provides an overview and in-depth analysis of recent advances in stability of linear systems with time-varying delays. First, recent developments of a delay convex analysis approach, a reciprocally convex approach and the construction of Lyapunov–Krasovskii functionals are reviewed insightfully. Second, in-depth analysis of the Bessel–Legendre inequality and some affine integral inequalities is made, and recent stability results are also summarised, including stability criteria for three cases of a time-varying delay, where information on the bounds of the time-varying delay and its derivative is totally known, partly known and completely unknown, respectively. Third, a number of stability criteria are developed for the above three cases of the time-varying delay by employing canonical Bessel–Legendre inequalities, together with augmented Lyapunov–Krasovskii functionals. It is shown through numerical examples that these stability criteria outperform some existing results. Finally, several challenging issues are pointed out to direct the near future research.
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an overview of recent developments in lyapunov Krasovskii functionals and stability criteria for recurrent neural networks with time varying delays
Neurocomputing, 2018Co-Authors: Xianming Zhang, Qinglong Han, Derui DingAbstract:Abstract Global asymptotic stability is an important issue for wide applications of recurrent neural networks with time-varying delays. The Lyapunov–Krasovskii functional method is a powerful tool to check the global asymptotic stability of a delayed recurrent neural network. When the Lyapunov–Krasovskii functional method is employed, three steps are necessary in order to derive a global asymptotic stability criterion: (i) constructing a Lyapunov–Krasovskii functional, (ii) estimating the derivative of the Lyapunov–Krasovskii functional, and (iii) formulating a global asymptotic stability criterion. This paper provides an overview of recent developments in each step with insightful understanding. In the first step, some existing Lyapunov–Krasovskii functionals for stability of delayed recurrent neural networks are anatomized. In the second step, a free-weighting matrix approach, an integral inequality approach and its recent developments, reciprocally convex inequalities and S-procedure are analyzed in detail. In the third step, linear convex and quadratic convex approaches, together with the refinement of allowable delay sets are reviewed. Finally, some challenging issues are presented to guide the future research.
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admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays
IEEE Transactions on Neural Networks, 2018Co-Authors: Xianming Zhang, Qinglong Han, Jun WangAbstract:This paper is concerned with global asymptotic stability of a neural network with a time-varying delay, where the delay function is differentiable uniformly bounded with delay-derivative bounded from above. First, a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions. This inequality provides a tighter bound in the form of a convex combination than some existing ones. Second, by constructing proper Lyapunov–Krasovskii functional, global asymptotic stability of the neural network is analyzed for two types of the time-varying delays depending on whether or not the lower bound of the delay derivative is known. Third, noticing that sufficient conditions on stability from estimation on the derivative of some Lyapunov–Krasovskii functional are affine both on the delay function and its derivative, allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study. Finally, two numerical examples are given to substantiate the effectiveness of the proposed method.
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An optimal reciprocally convex inequality and an augmented Lyapunov–Krasovskii functional for stability of linear systems with time-varying delay
Automatica, 2017Co-Authors: Xianming Zhang, Qinglong Han, Alexandre Seuret, Frédéric GouaisbautAbstract:This paper is concerned with stability of a linear system with a time-varying delay. First, an optimal reciprocally convex inequality is proposed. Compared with the extended reciprocally convex inequality recently reported, the optimal reciprocally convex inequality not only provides an optimal bound for the reciprocally convex combination, but also introduces less slack matrix variables. Second, a new Lyapunov-Krasovskii functional is tailored for the use of auxiliary function-based integral inequality. Third, based on the optimal reciprocally convex inequality and the new Lyapunov-Krasovskii functional, a stability criterion is derived for the system under study. Finally, two well-studied numerical examples are given to show that the obtained stability criterion can produce a larger upper bound of the time-varying delay than some existing methods.
