Stability analysis for stochastic BAM neural networks with Markovian jumping parameters

This paper is concerned with the stability analysis issue for stochastic delayed bidirectional associative memory (BAM) neural network with Markovian jumping parameters. Assume that the jumping parameters are generated from continue-time discrete-state homogeneous Markov process and the delays are time-invariant. By employing the Lyapunov stability theory, some inequality techniques and the stochastic analysis, sufficient conditions are derived to achieve the global exponential stability in the mean square of the stochastic BAM neural network. One example is also provided in the end of this paper to illustrate the effectiveness of our results.     

Delay dependent stability results for fuzzy BAM neural networks with Markovian jumping parameters

This paper deals with the delay-dependent asymptotic stability analysis problem for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying interval delays and Markovian jumping parameters by Takagi–Sugeno (T–S) fuzzy model. The nonlinear delayed BAM neural networks are first established as a modified T–S fuzzy model in which the consequent parts are composed of a set of Markovian jumping BAM neural networks with time-varying interval delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite-state space. The new type of Markovian jumping matrices P_k and Q_k are introduced in this paper. The parameter uncertainties are assumed to be norm bounded and the 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. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov–Krasovskii functional and introducing some free-weighting matrices. Numerical examples are given to demonstrate the effectiveness of the proposed methods.     

Global asymptotic stability of uncertain stochastic bi-directional associative memory networks with discrete and distributed delays

In this paper, the global asymptotic stability analysis problem is investigated for a class of stochastic bi-directional associative memory (BAM) networks with mixed time-delays and parameter uncertainties. The mixed time-delays consist of both the discrete and the distributed delays, the uncertainties are assumed to be norm-bounded, and the neural network are subject to stochastic disturbances described by a Brownian motion. Without assuming the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and some new developed techniques to establish sufficient conditions for the stochastic delayed BAM networks to be globally asymptotically stable in the mean square. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs) that can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.     

Design and economic optimization of shell-and-tube heat exchanger using cohort intelligence algorithm

In this paper, the stability analysis problem is investigated for a new class of discrete-time singular neural networks with Markovian jump and mixed time-delays. The jumping parameters are generated from a discrete-time homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The mixed time-delays are composed of discrete and distributed delays. The activation functions are not required to be strictly monotonic and be differentiable. The purpose of this paper is to derive some delay-dependent sufficient conditions such that the singular neural networks to be regular, causal and stochastically stable in the mean square. Finally, numerical examples are also provided to illustrate the effectiveness of the proposed methods.

     

Global Robust Exponential Stability of Interval General BAM Neural Network with Delays

In this paper, a class of interval general bidirectional associative memory (BAM) neural networks with delays are introduced and studied, which include many well-known neural networks as special cases. By using fixed point technic, we prove an existence and uniqueness of the equilibrium point for the interval general BAM neural networks with delays. By using a proper Lyapunov functions, we get a sufficient condition to ensure the global robust exponential stability for the interval general BAM neural networks with delays, and we just require that activation function is globally Lipschitz continuous, which is less conservative and less restrictive than the monotonic assumption in previous results. In the last section, we also give an example to demonstrate the validity of our stability result for interval neural networks with delays.     

Stochastic stability of uncertain fuzzy recurrent neural networks with Markovian jumping parameters

In this paper, the global robust stability of uncertain recurrent neural networks with Markovian jumping parameters which are represented by the Takagi–Sugeno fuzzy model is considered. A novel linear matrix inequality-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of uncertain fuzzy recurrent neural networks with Markovian jumping parameters. Finally, numerical examples are given to demonstrate the correctness of the theoretical results. Our results are also compared with results discussed in Arik [On the global asymptotic stability of delayed cellular neural networks, IEEE Trans. Circ. Syst. I 47 (2000), pp. 571–574], Cao [Global stability conditions for delayed CNNs, IEEE Trans. Circ. Syst. I 48 (2001), pp. 1330–1333] and Lou and Cui [Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters, J. Math. Anal. Appl. 328 (2007), pp. 316–326] to show the effectiveness and conservativeness.     

Mittag–Leffler Stability and Global Asymptotically $$\omega $$-Periodicity of Fractional-Order BAM Neural Networks with Time-Varying Delays

This article studies the Mittag–Leffler stability and global asymptotical \(\omega \)-periodicity for a class of fractional-order bidirectional associative memory (BAM) neural networks with time-varying delays by using Laplace transform, stability theory of fractional systems and some integration technique. Firstly, some sufficient conditions are given to ensure the boundedness and global Mittaag-Leffler stability of fractional-order BAM neural networks with time-varying delays. Next, S-asymptotical \(\omega \)-periodicity and global asymptotical \(\omega \)-periodicity of fractional-order BAM neural networks with time-varying delays are also explored. Finally, some numerical examples and simulation are performed to show the effectiveness of theoretical results.     

Delay-dependent <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control for a class of uncertain time-delay singular Markovian jump systems via hybrid impulsive control

This paper deals with the problem of robust normalization and delay-dependent H _∞ control for a class of singular Markovian jump systems with norm-bounded parameter uncertainties and time delay. A new impulsive and proportional-derivative control strategy with memory is presented, which results in a novel class of hybrid impulsive systems. Sufficient conditions are developed to guarantee that the resultant closed-loop system is not only robust normal and stochastically stable, but also satisfies a prescribed H _∞ performance level for all delays no larger than a given upper bound. In addition, the explicit expression of the desired impulsive control gains is also given together with the design approach. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.     

Decentralized Event-triggered Stability Analysis of Neutral-type BAM Neural Networks with Markovian Jump Parameters and Mixed Time Varying Delays

This paper investigates decentralized event-triggered stability analysis of neutral-type BAM neural networks with Markovian jump parameters and mixed time varying delays. We apply the decentralized event triggered approach to the bidirectional associative memory (BAM) neural networks to reduce the network traffic and the resource of computation. A bidirectional associative memory neural networks is constructed with the mixed time varying delays and Markov process parameters. The criteria for the asymptotically stability are proposed by using with the Lyapunov-Krasovskii functional method, reciprocal convex property and Jensen’s inequality. Stability condition of neutral-type BAM neural networks with Markovian jump parameters and mixed delays is established in terms of linear matrix inequalities. Finally three numerical examples are given to demonstrate the effectiveness of the proposed results     

Impulsive control of unstable neural networks with unbounded time-varying delays

This paper considers the impulsive control of unstable neural networks with unbounded time-varying delays, where the time delays to be addressed include the unbounded discrete time-varying delay and unbounded distributed time-varying delay. By employing impulsive control theory and some analysis techniques, several sufficient conditions ensuring μ-stability, including uniform stability, (global) asymptotical stability, and (global) exponential stability, are derived. It is shown that an unstable delay neural network, especially for the case of unbounded time-varying delays, can be stabilized and has μ-stability via proper impulsive control strategies. Three numerical examples and their simulations are presented to demonstrate the effectiveness of the control strategy.     

Exponential stability and periodic oscillatory solution in BAMnetworks with delays

Both exponential stability and periodic oscillatory solution of bidirectional associative memory (BAM) networks with axonal signal transmission delays are considered by constructing suitable Lyapunov functional and some analysis techniques. Some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of BAM with delays. These conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for BAM with delays. In addition, two examples are given to illustrate the results.     

Global Robust Exponential Stability of Interval BAM Neural Network with Mixed Delays under Uncertainty

In this paper, a class of interval bidirectional associative memory (BAM) neural networks with mixed delays under uncertainty are introduced and studied, which include many well-known neural networks as special cases. The mixed delays mean the simultaneous presence of both the discrete delay, and the distributive delay. Furthermore, the parameter of matrix is taken values in a interval and controlled by a unknown, but bounded function. By using a suitable Lyapunov–Krasovskii function with the linear matrix inequality (LMI) technique, we obtain a sufficient condition to ensure the global robust exponential stability for the interval BAM neural networks with mixed delays under uncertainty, which is more generalized and less conservative, restrictive than previous results. In the last section, the validity of our stability result is demonstrated by a numerical example.     

Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity

This paper is concerned with the problem of robust exponential stability for a class of hybrid stochastic neural networks with mixed time-delays and Markovian jumping parameters. In this paper, free-weighting matrices are employed to express the relationship between the terms in the Leibniz–Newton formula. Based on the relationship, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions for the mixed time-delays neural networks with Markovian jumping parameters. Finally, two simulation examples are provided to demonstrate the effectiveness of the results developed.     

Stability of stochastic Markovian jump neural networks with mode-dependent delays

In this paper, the problem of stability analysis for a general class of uncertain stochastic neural networks with Markovian jumping parameters and mixed mode-dependent delays is considered. By the use of a new Markovian switching Lyapunov–Krasovskii functional, delay-dependent conditions on mean square asymptotic stability are derived in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed approach.     

Dissipativity and passivity analysis of Markovian jump impulsive neural networks with time delays

This paper discusses the issue of dissipativity and passivity analysis for a class of impulsive neural networks with both Markovian jump parameters and mixed time delays. The jumping parameters are modelled as a continuous-time discrete-state Markov chain. Based on a multiple integral inequality technique, a novel delay-dependent dissipativity criterion is established via a suitable Lyapunov functional involving the multiple integral terms. The proposed dissipativity and passivity conditions for the impulsive neural networks are represented by means of linear matrix inequalities. Finally, three numerical examples are given to show the effectiveness of the proposed criteria.     

Exponential synchronization of stochastic chaotic neural networks with mixed time delays and Markovian switching

This paper studies the exponential synchronization problem for a class of stochastic perturbed chaotic neural networks with both Markovian jump parameters and mixed time delays. The mixed delays consist of discrete and distributed time-varying delays. At first, based on a Halanay-type inequality for stochastic differential equations, by virtue of drive-response concept and time-delay feedback control techniques, a delay-dependent sufficient condition is proposed to guarantee the exponential synchronization of two identical Markovian jumping chaotic-delayed neural networks with stochastic perturbation. Then, by utilizing the Jensen integral inequality and a novel Lemma, another delay-dependent criterion is established to achieve the globally stochastic robust synchronization. With some parameters being fixed in advance, these conditions can be solved numerically by employing the Matlab software. Finally, a numerical example with their simulations is provided to illustrate the effectiveness of the presented synchronization scheme.     

Stochastic coalitional better-response dynamics and stable equilibrium

We consider coalition formation among players in an n-player finite strategic game over infinite horizon. At each time a randomly formed coalition makes a joint deviation from a current action profile such that at new action profile all the players from the coalition are strictly benefited. Such deviations define a coalitional better-response (CBR) dynamics that is in general stochastic. The CBR dynamics either converges to a K-stable equilibrium or becomes stuck in a closed cycle. We also assume that at each time a selected coalition makes mistake in deviation with small probability that add mutations (perturbations) into CBR dynamics. We prove that all K-stable equilibria and all action profiles from closed cycles, that have minimum stochastic potential, are stochastically stable. Similar statement holds for strict K-stable equilibrium. We apply the CBR dynamics to study the dynamic formation of the networks in the presence of mutations. Under the CBR dynamics all strongly stable networks and closed cycles of networks are stochastically stable.     

Finite Time <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Boundedness of Discrete-time Markovian Jump Neural Networks with Time-varying Delays

This paper is concerned with the problem of finite-time H_∞ boundedness of discrete-time Markovian jumping neural netwoks with time-varying delays. A new sufficient condition is presented which guarantees the stability of the closed-loop system and the same time maximizes the boundedness on the non-linearity. An extension of fixed transition probability Markovian model is combined to time-varying transition probabilities has offered. By constructing a novel Lyapunov-Krasovskii functional, the system under consideration is subject to interval timevarying delay and norm-bounded disturbances. Linear matrix inequality approach is used to solve the finite-time stability problem. Numerical example is given to illustrate the effectiveness of the proposed result.     

Globally exponential stability and stabilization of interconnected Markovian jump system with mode-dependent delays

This paper focuses on the problems of globally exponential stability and stabilization with H_∞ performance for a class of interconnected Markovian jump system with mode-dependent delays in interconnection. By constructing a Lyapunov-Krasovskii functional, delay-range-dependent globally mean-square exponential stability conditions are established in terms of linear matrix inequalities. Based on the obtained conditions, state feedback control utilizing global state information and state feedback control utilizing global state information of decentralised observers are developed to render the closed-loop interconnected Markovian jump time-delay system globally exponential stable with H_∞ performance. Numerical simulation of a power system, composed of three coupled machines, is used to illustrate the effectiveness of the obtained results.