Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this paper, the problem of stability analysis for a class of impulsive stochastic Cohen–Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen–Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.This work was supported by the Natural Science Foundation of CQ CSTC under grant 2007BB0430, the Scientific Research Fund of Chongqing Municipal Education Commission under Grant KJ070401, an International Joint Project sponsored by the Royal Society of the UK and the National Natural Science Foundation of China, and the Alexander von Humboldt Foundation of Germany

Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2013 IEEE.In this paper, the synchronization problem is studied for an array of N identical delayed neutral-type neural networks with Markovian jumping parameters. The coupled networks involve both the mode-dependent discrete-time delays and the mode-dependent unbounded distributed time delays. All the network parameters including the coupling matrix are also dependent on the Markovian jumping mode. By introducing novel Lyapunov-Krasovskii functionals and using some analytical techniques, sufficient conditions are derived to guarantee that the coupled networks are asymptotically synchronized in mean square. The derived sufficient conditions are closely related with the discrete-time delays, the distributed time delays, the mode transition probability, and the coupling structure of the networks. The obtained criteria are given in terms of matrix inequalities that can be efficiently solved by employing the semidefinite program method. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 61074129, 61174136 and 61134009, and the Natural Science Foundation of Jiangsu Province of China under Grants BK2010313 and BK2011598

Robust Exponential Stabilization of Stochastic Delay Interval Recurrent Neural Networks with Distributed Parameters and Markovian Jumping by Using Periodically Intermittent Control

We consider a class of stochastic delay recurrent neural networks with distributed parameters and Markovian jumping. It is assumed that the coefficients in these neural networks belong to the interval matrices. Several sufficient conditions ensuring robust exponential stabilization are derived by using periodically intermittent control and Lyapunov functional. The obtained results are very easy to verify and implement, and improve the existing results. Finally, an example with numerical simulations is given to illustrate the presented criteria

Multidimensional Taylor Network Optimal Control of MIMO Nonlinear Systems without Models for Tracking by Output Feedback

The actual controlled objects are generally multi-input and multioutput (MIMO) nonlinear systems with imprecise models or even without models, so it is one of the hot topics in the control theory. Due to the complex internal structure, the general control methods without models tend to be based on neural networks. However, the neuron of neural networks includes the exponential function, which contributes to the complexity of calculation, making the neural network control unable to meet the real-time requirements. The newly developed multidimensional Taylor network (MTN) requires only addition and multiplication, so it is easy to realize real-time control. In the present study, the MTN approach is extended to MIMO nonlinear systems without models to realize adaptive output feedback control. The MTN controller is proposed to guarantee the stability of the closed-loop system. Our experimental results show that the output signals of the system are bounded and the tracking error goes nearly to zero. The MTN optimal controller is proven to promise far better real-time dynamic performance and robustness than the BP neural network self-adaption reconstitution controller

Spectral Perspective on the Stability of Discrete-Time Markov Jump Systems with Multiplicative Noise

We apply the spectrum analysis approach to address the stability of discrete-time Markov jump systems with state-multiplicative noise. In terms of the spectral distribution of a generalized Lyapunov operator, spectral criteria are presented to testify three different kinds of stochastic stabilities: asymptotic mean square stability, critical stability, and essential instability

Finite-Time Boundedness of Markov Jump System with Piecewise-Constant Transition Probabilities via Dynamic Output Feedback Control

This paper first investigates the problem of finite-time boundedness of Markovian jump system with piecewise-constant transition probabilities via dynamic output feedback control, which leads to both stochastic jumps and deterministic switches. Based on stochastic Lyapunov functional, the concept of finite-time boundedness, average dwell time, and the coupling relationship among time delays, several sufficient conditions are established for finite-time boundedness and H∞ filtering finite-time boundedness. The system trajectory stays within a prescribed bound. Finally, an example is given to illustrate the efficiency of the proposed method

An analysis of stability of a class of neutral-type neural networks with discrete time delays

The problem of existence, uniqueness, and global asymptotic stability is considered for the class of neutral-type neural network model with discrete time delays. By employing a suitable Lyapunov functional and using the homeomorphism mapping theorem, we derive some new delay-independent sufficient conditions for the existence, uniqueness, and global asymptotic stability of the equilibrium point for this class of neutral-type systems. The obtained conditions basically establish some norm and matrix inequalities involving the network parameters of the neural system. The main advantage of the proposed results is that they can be expressed in terms of network parameters only. Some comparative examples are also given to compare our results with the previous corresponding results and demonstrate the effectiveness of the results presented.Publisher's Versio