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In this paper, we investigate the permanence of a class of Holling III-Tanner predator-prey diffusion system with stocking rate and time delay, the existence positive periodic solution by using Comparability Theorem, Coincidence Degree Theory. We obtain the sufficient conditions which guarantee permanent of the system and existence of the positive periodic solution of the periodic system. Some new...
In this paper, we investigate the persistence of a class environment mathematical model with delays, the existence and the global stability of its global positive periodic solution by using Comparability Theorem, Coincidence Degree Theory and Lyapunov functions. We obtain the sufficient conditions which guarantee the existence of the global asymptotic stable positive periodic solution of the periodic...
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 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 is concerned with the stabilization problem of discrete-time systems with stochastic sampling. It is assumed that there are a single-rate sampling in the plant input and two stochastic sampling rates in the controller input whose occurrence probabilities are given constants and satisfy a Bernoulli distribution. By Lyapunov function approach, a new sufficient condition is presented for the...
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...
This paper deals with the problem of delay-dependent robust stability for a class of uncertain stochastic recurrent neural networks (USRNNs) with discrete and distributed delays. In such systems, both parameter uncertainties and stochastic perturbations are taken into account. The parameter uncertainties are norm-bounded and the stochastic perturbations are in the form of a Brownian motion. Based...
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...
In this paper, we will consider the problems where observation delay is time-varying and design distributed estimators by combining a consensus strategy. The optimal local estimator for every node with time-varying observation delay is first designed, which plays an important role in the distributed estimator design. Then the optimal distributed estimator for any choice of the consensus gain is proposed...
This paper discusses the robustness of nonlinear model predictive control (NMPC) based on sub-optimal solution obtained under reduced precision solution (RPS) criteria. NMPC needs to solve the optimal control problem (OCP) quickly and the input is injected to the controlled plant in time. Traditional convergence criteria in optimization algorithms usually cost excessive long computation time with...
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 is concerned with exponential estimates for a class of continuos-time singular Markovian jump systems with time-varying delays. By constructing a decay-rate-dependent stochastic Lyapunov-Krasovskii function and utilizing slow-fast decomposition technique, an exponential admissibility condition, which not only guarantees the regularity, non-impulsiveness and exponential stability of the...
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...
In this paper, an-LMI approach is utilized for the stabilization of Discrete-Time Delay Nonlinear Systems (DTDNS). The delay provided is state-delay. The control criterion is derived in terms of linear matrix inequalities (LMI's). The controller is designed by making use of back stepping technique. By choosing an appropriate Lyapunov function, some mathematical manipulations have been carried out...
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.
This paper is concerned with the method of impulsive controller design for linear systems with multiple-packet transmission. First, the mathematic model of respond closed-loop is built in terms of linear impulsive systems description. Second, on the basis of guaranteeing closed loop systems stability, the design method of the impulsive feedback controller and the design procedure are given. Finally,...
A three stage-structured prey-predator model with hunting delay is studied. The characteristic equations of the boundary and positive equilibrium are analyzed and the conditions of the positive equilibrium occurring Hopf bifurcation are given by applying the theorem of Hopf bifurcation. By using Nyquist criterion, the estimation of the length of delay to preserve stability is obtained. Finally, numerical...
This paper is concerned with analysis problem for the stability of the a stochastic discrete-time neural networks (DNNs) with discrete time-varying delay. By used some novel analysis techniques, stability theory and Lyapunov -Krasovskii function, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally asymptotically stable in mean square...
The paper investigates the problem of robust stability for a class of continuous-time uncertain switched singular systems with multiple-state delays. By the state transformation and a proper Lyapunov-Krasovskii functional, the robust stability criteria and switching law are given.
The problem of delay-dependent asymptotic stability criteria for neural networks with time-varying delays is investigated. An improved delay dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs) to ensure a large upper bound for time-delay. A new class of Lyapunov functional is constructed and the known bounds of the delay interval is split in two subintervals to...
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