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This paper is concerned with the problem of stability of systems with time-varying delay in a given interval. A novel Lyapunov-Krasovskii functional is proposed to obtain new stability conditions. Some triple integral terms are introduced in the Lyapunov-Krasovskii functional and the information on the lower bound on the delay are sufficiently used. New delay-dependent stability criteria are derived...
This paper addresses the robust stability analysis problem of T-S fuzzy systems with interval time-varying delays. In the derivation, this paper provides a useful relaxation technique to obtain a less conservative stability criterion from an appropriate Lyapunov-Krasovskii functional dependent on fuzzy weighting functions.
This paper focuses on the absolute stability of a new class of Takagi-Sugeno (T-S) fuzzy Lurie control systems with time-delay and time-variant uncertainties in the state as well as the nonlinearity functions. Based on Lyapunov-Krasovskii functional (LKF) together with linear matrix inequality (LMI) approach, a novel delay-dependent absolute stability criterion is derived. In the end, a numerical...
The notion of integral input-to-state stability (integral-ISS) is now recognized as a central concept in nonlinear systems analysis. In this work, we explore the Razumikhin approach to the integral-ISS property for systems with delays. The main idea is to treat the delayed state variable as a disturbance input. The results in this work extend the previous results on the Razumikhin method in the contexts...
This paper is concerned with robust stability problem for Markovian jump singular time-delay systems with disturbances. In terms of strict linear matrix inequality(LMI), a new necessary and sufficient condition is proposed for the unforced Markovian jump singular system to be stochastically admissible. Based on this, the sufficient conditions are obtained for the existence of performance, which guarantees...
This paper discusses stability of neural networks (NNs) with time-varying delay. Delay-fractioning Lyapunov-Krasovskii functional (LKF) method and convex analysis are applied to establish a new stability condition. Two possible cases for the delay are taken into account when the delay interval is equivalently divided into two subintervals. The maximal allowable delay that ensures global asymptotical...
This paper investigates robust stability of reset control systems with both uncertainties and transmission delays. Firstly, a generalized Lyapunov-Krasovskii theorem is proven. Secondly, the technique of parameter-dependent full-rank right annihilator of matrices is used to deal with the uncertain reset time instants caused by output matrix uncertainties. Based on this, several necessary and sufficient...
This paper gives new contributions to the area of non-Lyapunov (finite time stability, technical stability, practical stability, final stability) for the particular class of linear discrete time delay systems. The idea of attractive practical stability is introduced for the first time. Moreover, based on the matrix inequalities and Lyapunov-like functions, some new sufficient conditions under which...
In this paper, the problem of exponential stabilization of neutral-type neural networks with various activation functions and interval non-differentiable and distributed time-varying delays is considered. The interval time-varying delay function is not necessary to be differentiable. By constructing a set of improved Lyapunov-Krasovskii functional combined with Leibniz-Newton's formula, the proposed...
Dynamical behavior of neutral neural networks with distributed delays is studied by employing suitable Lyapunov functional, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical neutral neural networks with time delay and some novel asymptotic stability criteria are also derived. The obtained conditions...
Dynamical behavior of neutral neural networks with distributed delays is studied by employing suitable Lyapunov functionals, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical neutral neural networks with time delay and some novel asymptotic stability criteria are also derived. The obtained conditions...
This paper discusses the synchronization problem for a class of Lurie type complex dynamical networks with time-varying delay. Based on a Lyapunov-Krasovskii functional, some new delay-dependent synchronization criteria are derived in the form of linear matrix inequalities by employing a delay decomposition and free matrix method. And a strategy for synchronization is presented based on a linear feedback...
In this paper, exponential stability criteria of linear neutral systems with/ without uncertainties are investigated. By applying a change of variable, the Leibniz-Newton formula, integral inequalities and Lyapunov-Krasovskii functionals without adding free matrices, improved exponential stability-delay dependent criteria of the systems are obtained in the form of linear matrix inequality (LMI). At...
In order to alleviate the conservativeness of the robust stability criterion, the delay-dependent stability problem for uncertain T-S fuzzy time-delay systems with interval time-varying delay is to be investigated in this paper. A new Lyapunov-Krasovskii function and a further improved free-weighing matrix approach are used to analyze the stability. A new less conservative robust stability criterion...
The heavy tailed nature in dynamic spectrum networks challenges the applicability of conventional network stability criterions. To encounter this, a new stability criterion, namely moment stability, is introduced, which requires that the queue length of each secondary user has finite moments for every achievable order. Then, the necessary and sufficient conditions for the existence of a resource allocation...
This paper, the robust stability problem of dynamic interval systems with multiple time-delays is considered. Firstly, a kind of equivalent description of the interval matrix is presented. Then by using Lyapunov stability theory and matrix measure approach, several simple sufficient conditions of robust stability for dynamic continuous and discrete interval systems with multiple time-delays are obtained,...
The ultimate boundedness is one of foundational concepts, which plays an important role in investigating the global asymptotic stability, its control and synchronization for dynamical systems. The ultimate boundedness of stochastic Cohen-Grossberg neural networks with time-varying delays is investigated. By employing Lyapunov method and matrix technique, some novel results and criteria on stochastic...
Power system may not return to its original status and become unstable when subjected to small signal disturbance. Conventional small signal stability (SSS) theory is based on linear control system model without time delay and thus it is not fit for power system stability analysis and stabilization design when relatively larger signal transmission delay exists. In order to overcome the limitations...
This paper is concerned with the problem of robust stability of uncertain neutral systems with distributed delays. By Construct a new Lyapunov-Krasovskii functional, using the idea of discrete delay decomposition, delay decomposition approach is adopted both in discrete delay and distribute delay, combined with new Jensen inequality, improved discrete-, distributed delay-dependent stability conditions...
This paper presents an algebraic criterion for the input-to-state stability (ISS) of recurrent neural networks with Markovian switching. The criterion is easy to be verified with the connection weights. A numerical example is given to demonstrate the effectiveness of the proposed criteria.
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