Delayed-state-feedback exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays

This paper studies the problem of the robustly exponential stabilization for uncertain Markovian jump systems with mode-dependent time-varying state delays. The contribution of this paper is two-fold. Firstly, by constructing a modified Lyapunov functional and using free-weighting matrices technique, some delay-dependent robustly exponential stability criteria of such systems are obtained in terms of linear matrix inequalities (LMIs), which are less conservative than some existing ones. Secondly, a state feedback controller is designed, which can guarantee the robustly exponential stability of the uncertain closed-loop systems. Some illustrative numerical examples are given to demonstrate the reduced conservatism and applicability of the obtained results.     

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

In this paper, we are concerned with the synchronization problem of a class of stochastic reaction-diffusion neural networks with time-varying delays and Dirichlet boundary conditions. By using the Lyapunov–Krasovskii functional method, feedback control approach and stochastic analysis technology, delay-dependent synchronization conditions including the information of reaction-diffusion terms are presented, which are expressed in terms of linear matrix inequalities (LMIs). The feedback controllers can be constructed by solving the derived LMIs. Finally, illustrative examples are given to show the effectiveness of the proposed technique.     

Finite-time synchronization control for uncertain Markov jump neural networks with input constraints

This paper is concerned with the problem of finite-time synchronization control for uncertain Markov jump neural networks in the presence of constraints on the control input amplitude. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. By using a parameter-dependent Lyapunov functional and a simple matrix decoupling method, a sufficient condition is proposed to ensure that the considered networks are stochastically synchronized over a finite-time interval. The desired mode-independent controller parameters can be computed via solving a convex optimization problem. Finally, two chaos neural networks are employed to demonstrate the effectiveness of our proposed approach.     

Global exponential stability for quaternion-valued recurrent neural networks with time-varying delays

Nonlinear Dynamics - In this paper, we employ a novel method for solving the problem of the global exponential stability of quaternion-valued recurrent neural networks (QVNNs) with time-varying...     

Globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching

The problem of globally exponential stability of stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching is studied in this paper. By using the Lyapunov?CKrasovskii method and the stochastic analysis approach, a sufficient condition to ensure globally exponential stability for the stochastic neutral-type delayed neural networks with impulsive perturbations and Markovian switching is derived. Finally, a numerical example is given to illustrate the effectiveness of the result proposed in this paper.     

Global exponential stability of stochastic memristor-based complex-valued neural networks with time delays

In recent years, the dynamic behaviors of complex-valued neural networks have been extensively investigated in a variety of areas. This paper focuses on the stability of stochastic memristor-based complex-valued neural networks with time delays. By using the Lyapunov stability theory, Halanay inequality and Itô formula, new sufficient conditions are obtained for ensuring the global exponential stability of the considered system. Moreover, the obtained results not only generalize the previously published corresponding results as special cases for our results, but also can be checked with the parameters of system itself. Finally, simulation results in three numerical examples are discussed to illustrate the theoretical results.     

GLOBAL EXPONENTIAL STABILITY OF HOPFIELD NEURAL NETWORKS WITH VARIABLE DELAYS AND IMPULSIVE EFFECTS

A class of Hopfield neural network with time-varying delays and impulsive effects is concerned. By applying the piecewise continuous vector Lyapunov function some sufficient conditions were obtained to ensure the global exponential stability of impulsive delay neural networks. An example and its simulation are given to illustrate the effectiveness of the results.     

Sampled-data state estimation for delayed neural networks with Markovian jumping parameters

This paper is concerned with the sampled-data state estimation problem for a class of delayed neural networks with Markovian jumping parameters. Unlike the classical state estimation problem, in our state estimation scheme, the sampled measurements are adopted to estimate the concerned neuron states. The neural network under consideration is assumed to have multiple modes that switch from one to another according to a given Markovian chain. By utilizing the input delay approach, the sampling period is converted into a time-varying yet bounded delay. Then a sufficient condition is given under which the resulting error dynamics of the neural networks is exponentially stable in the mean square. Based on that, a set of sampled-data estimators is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using the available software. Finally, a numerical example is used to show the effectiveness of the estimation approach proposed in this paper.     

Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

The robust observer problem is considered in this paper for a class of discrete-time neural networks with Markovian jumping parameters and mode-dependent time delays which are in both discrete-time form and finite distributed form. The neural network switches from one mode to another controlled by a Markov chain with known transition probability. Time-delays considered in this paper are mode-dependent which may reflect a more realistic version of the neural network. By using the Lyapunov functional method and the techniques of linear matrix inequalities (LMIs), sufficient conditions are established in terms of LMIs that ensure the existence of the robust observer. The obtained conditions are easy to be verified via the LMI toolbox. An example is presented to show the effectiveness of the obtained results.     

State estimation for Markovian jumping recurrent neural networks with interval time-varying delays

The paper is concerned with the state estimation problem for a class of neural networks with Markovian jumping parameters. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error are globally stable in the mean square. A new type of Markovian jumping matrix P _i is introduced in this paper. The discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Delay-independent exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms

Different from the approaches used in the earlier papers, in this paper, the Halanay inequality technique, in combination with the Lyapunov method, is exploited to establish a delay-independent sufficient condition for the exponential stability of stochastic Cohen–Grossberg neural networks with time-varying delays and reaction–diffusion terms. Moreover, for the deterministic delayed Cohen–Grossberg neural networks, with or without reaction–diffusion terms, sufficient criteria for their global exponential stability are also obtained. The proposed results improve and extend those in the earlier literature and are easier to verify. An example is also given to illustrate the correctness of our results.     

Global asymptotic stability for Hopfield-type neural networks with diffusion effects

The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique.     

Output-feedback control for singular Markovian jump systems with input saturation

This paper considers the problem of dynamic output-feedback stabilization for singular Markovian jump systems with input saturation. The stabilization and set invariance conditions are first formulated in terms of non-convex matrix inequalities which is not linear matrix inequalities (LMIs). This paper, however, successfully derives the necessary and sufficient conditions for the non-convex inequalities in terms of LMIs. Also, an optimization problem is formulated to find the largest contractively invariant set in mean square sense of the closed-loop systems. Two numerical examples show the validity of the derived results.     

Passivity analysis of uncertain neural networks with mixed time-varying delays

This paper addresses the passivity problem for uncertain neural networks with both discrete and distributed time-varying delays. It is assumed that the parameter uncertainties are norm-bounded. By construction of an augmented Lyapunov–Krasovskii functional and utilization of zero equalities, improved passivity criteria for the networks are derived in terms of linear matrix inequalities (LMIs) via new approaches. Through three numerical examples, the effectiveness to enhance the feasible region of the proposed criteria is demonstrated.     

Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions

In this paper, the global robust exponential stability of interval neural networks with delays and inverse Hölder neuron activation functions is considered. By using linear matrix inequality (LMI) techniques and Brouwer degree properties, the existence and uniqueness of the equilibrium point are proved. By applying Lyapunov functional approach, a sufficient condition which ensures that the network is globally robustly exponentially stable is established. A numerical example is provided to demonstrate the validity of the theoretical results.     

On improved passivity criteria of uncertain neural networks with time-varying delays

In this paper, the problem of passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii’s functional and some novel analysis techniques, improved delay-dependent criteria for checking the passivity of the neural networks are established. The proposed criteria are represented in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.     

Asynchronous observer-based finite-time control for nonlinear Markovian jump systems with time-varying delays

Nonlinear Dynamics - This paper addresses the problem of finite-time observer-based control for continuous-time nonlinear Markovian jump systems with time-varying delays. The existing studies about...