Extended dissipative analysis of generalized Markovian switching neural networks with two delay components

Sampled-Data Synchronization of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

In this article, sampled-data synchronization problem for stochastic Markovian jump neural networks (SMJNNs) with time-varying delay under aperiodic sampled-data control is considered. By constructing mode-dependent one-sided loop-based Lyapunov functional and mode-dependent two-sided loop-based Lyapunov functional and using the Itô formula, two different stochastic stability criteria are proposed for error SMJNNs with aperiodic sampled data. The slave system can be guaranteed to synchronize with the master system based on the proposed stochastic stability conditions. Furthermore, two corresponding mode-dependent aperiodic sampled-data controllers design methods are presented for error SMJNNs based on these two different stochastic stability criteria, respectively. Finally, two numerical simulation examples are provided to illustrate that the design method of aperiodic sampled-data controller given in this article can effectively stabilize unstable SMJNNs. It is also shown that the mode-dependent two-sided looped-functional method gives less conservative results than the mode-dependent one-sided looped-functional method.

Quantized control for extended dissipative synchronization of chaotic neural networks: A discretized LKF method

This work focuses on the extended dissipative synchronization problem for chaotic neural networks with time delay under quantized control. The discretized Lyapunov-Krasovskii functional method, in combination with the free-weighting matrix approach, is employed to obtain an analysis result of the extended dissipativity with low conservatism. Then, with the help of several decoupling methods, a computationally tractable design approach is proposed for the needed quantized controller. Finally, two examples are provided to illustrate the usefulness of the present analysis and design methods, respectively.

Finite-time non-fragile extended dissipative control for T-S fuzzy system via augmented Lyapunov-Krasovskii functional

The problem of non-fragile control for T-S fuzzy systems with parameter uncertainties is investigated in this paper. The focus is to construct an augmented Lyapunov-Krasovskii functional(LKF), single integral terms are processed by the method of an improved reciprocally convex inequality and integration by parts, which is derived to a new ht-depended stability criteria that finite-time bounded with extended dissipative for the closed-loop system. Furthermore, by using the linear matrix inequalities(LMIs), we can get the desired gain matrices of T-S fuzzy system. It is worth noting that these condition can derive to less conservative results than those existing approaches. And numerical examples are used to demonstrate the feasibility and superiority of the results.

H∞ State Estimation for Neural Networks With General Activation Function and Mixed Time-Varying Delays

This article deals with H_∞ state estimation of neural networks with mixed delays. In order to make full use of delay information, novel delay-product Lyapunov-Krasovskii functional (LKF) by using parameterized delay interval is first constructed. Then, generalized free-weighting-matrix integral inequality is used to estimate the derivative of LKF to reduce the conservatism. Also, a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model. Finally, sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed H_∞ performance. Numerical examples are simulated to show the benefits of our proposed method.

Bifurcations in a fractional-order BAM neural network with four different delays

This paper illuminates the issue of bifurcations for a fractional-order bidirectional associative memory neural network(FOBAMNN) with four different delays. On account of the affirmatory presumption, the developed FOBAMNN is firstly transformed into the one with two nonidentical delays. Then the critical values of Hopf bifurcations with respect to disparate delays are calculated quantitatively by establishing one delay and selecting remaining delay as a bifurcation parameter in the transformed model. It detects that the stability of the developed FOBAMNN with multiple delays can be fairly preserved if selecting lesser control delays, and Hopf bifurcation emerges once the control delays outnumber their critical values. The derived bifurcation results are numerically testified via the bifurcation graphs. The feasibility of theoretical analysis is ultimately corroborated in the light of simulation experiments. The analytic results available in this paper are beneficial to give impetus to resolve the issues of bifurcations of high-order FONNs with multiple delays.

Quasi-Synchronization and Bifurcation Results on Fractional-Order Quaternion-Valued Neural Networks

In this article, the quasi-synchronization and Hopf bifurcation issues are investigated for the fractional-order quaternion-valued neural networks (QVNNs) with time delay in the presence of parameter mismatches. On the basis of noncommutativity property of quaternion multiplication results, the quaternion network has been split as four real-valued networks. A synchronization theorem for fractional-order QVNNs is derived by employing suitable Lyapunov functional candidate; furthermore, the bifurcation behavior of the hub-structured fractional-order QVNNs with time delay has been investigated. Finally, two numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Estimation of Domain of Attraction for Aperiodic Sampled-Data Switched Delayed Neural Networks Subject to Actuator Saturation

In this paper, for the case of the asynchronous switching caused by that subsystem's switching occuring during a sampling interval, the domain of attraction estimation problem is investigated for aperiodic sampled-data switched delayed neural networks (ASDSDNNs) subject to actuator saturation. A parameters-dependent time-scheduled Lyapunov functional consisting of a novel looped-functional is constructed using segmentation technology and linear interpolation. By employing this novel functional and using an average dwell time (ADT) approach, exponential stability criteria are proposed for polytopic uncertain ASDSDNNs subject to actuator saturation. And a relationship between ADT and sampling period is revealed for ASDSDNNs. As a corollary, exponential stability criteria are proposed for nominal ASDSDNNs subject to actuator saturation. Furthermore, by describing the domain of attraction as a time-varying ellipsoid determined by the time-scheduled Lyapunov matrix, the proposed theoretical conditions are transformed into a linear matrix inequality (LMI)-based multi-objective optimization problem. The dynamic estimates of the domain of attraction for ASDSDNNs are solved. Numerical simulation examples are provided to illustrate the effectiveness of the proposed method.

Finite-time synchronization of memristor neural networks via interval matrix method

In this paper, the finite-time synchronization problems of two types of driven-response memristor neural networks (MNNs) without time-delay and with time-varying delays are investigated via interval matrix method, respectively. Based on interval matrix transformation, the driven-response MNNs are transformed into a kind of system with interval parameters, which is different from the previous research approaches. Several sufficient conditions in terms of linear matrix inequalities (LMIs) are driven to guarantee finite-time synchronization for MNNs. Correspondingly, two types of nonlinear feedback controllers are designed. Meanwhile, the upper-bounded of the settling time functions are estimated. Finally, two numerical examples with simulations are given to illustrate the correctness of the theoretical results and the effectiveness of the proposed controllers.

Extended Dissipativity Analysis for Markovian Jump Neural Networks With Time-Varying Delay via Delay-Product-Type Functionals

This paper investigates the problem of extended dissipativity for Markovian jump neural networks (MJNNs) with a time-varying delay. The objective is to derive less conservative extended dissipativity criteria for delayed MJNNs. Toward this aim, an appropriate Lyapunov-Krasovskii functional (LKF) with some improved delay-product-type terms is first constructed. Then, by employing the extended reciprocally convex matrix inequality (ERCMI) and the Wirtinger-based integral inequality to estimate the derivative of the constructed LKF, a delay-dependent extended dissipativity condition is derived for the delayed MJNNs. An improved extended dissipativity criterion is also given via the allowable delay sets method. Based on the above-mentioned results, the extended dissipativity condition of delayed NNs without Markovian jump parameters is directly derived. Finally, three numerical examples are employed to illustrate the advantages of the proposed method.

Reachable set estimation for Markovian jump neural networks with time-varying delay

This paper is concerned with the reachable set estimation for Markovian jump neural networks with time-varying delay and bounded peak inputs. The objective is to find a description of a reachable set that is containing all reachable states starting from the origin. In the framework of Lyapunov-Krasovskii functional method, an appropriate Lyapunov-Krasovskii functional is constructed firstly. Then by using the Wirtinger-based integral inequality and the extended reciprocally convex matrix inequality, an ellipsoidal description of the reachable set for the considered neural networks is derived. Finally, a numerical example with simulation results is provided to verify the effectiveness of our results.