Dynamics of impulsive neutral-type BAM neural networks

In this letter, the existence and the global exponential stability of piecewise pseudo almost periodic solutions (PAP_T) for bidirectional associative memory neural networks (BAMNNs) with time-varying delay in leakage (or forgetting) terms and impulsive are investigated by applying contraction mapping fixed point theorem, the exponential dichotomy of linear differential equations and differential inequality techniques. Furthermore, we give an explanatory example to illustrate the efficiency of the theoretical predictions.     

Stability analysis of almost periodic solutions of discontinuous BAM neural networks with hybrid time-varying delays and D operator

In the paper, we are concerned with a class of discontinuous BAM neural networks with hybrid time-varying delays and D operator. Based on the concept of Filippov solution, by means of the differential inclusions theory and the non-smooth analysis theory with Lyapunov-like approach, some new and novel sufficient conditions are derived to guarantee the existence, uniqueness and global exponential stability of almost-periodic solution of our proposed neural network model. To the authors’ knowledge, the results established in the paper are the only available results on the BAM neural networks, connecting the three main characteristics, i.e., discontinuous activation functions, hybrid time-varying delays and D operator. Some previous works in the literature are significantly extend and complement. Finally, two topical simulation examples are given to show the effectiveness of the established main results.     

Novel global robust exponential stability criterion for uncertain inertial-type BAM neural networks with discrete and distributed time-varying delays via Lagrange sense

In this paper, the global robust exponential stability problem for a class of uncertain inertial-type BAM neural networks with both time-varying delays is focused through Lagrange sense. The existence of time-varying delays in discrete and distributed terms is explored with the availability of lower and upper bounds of time-varying delays. Firstly, we transform the proposed inertial BAM neural networks to usual one. Secondly, by the aid of LKF, stability theory, integral inequality, some novel sufficient conditions for the global robust exponential stability of the addressed neural networks are obtained in terms of linear matrix inequalities, which can be easily tested in practice by utilizing LMI control toolbox in MATLAB software. Furthermore, many comparisons of proposed work are listed with some existing literatures to get less conservatism. Finally, two numerical examples are provided to demonstrate the advantages and superiority of our theoretical outcomes.     

Robust finite-time stability of singular nonlinear systems with interval time-varying delay

The problem of robust finite-time stability (RFTS) for singular nonlinear systems with interval time-varying delay is studied in this paper. Some delay-dependent sufficient conditions of RFTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii functional (LKF) method and singular analysis technique. Two examples are provided to show the applications of the proposed criteria.     

General synchronization criteria for nonlinear Markovian systems with random delays

It is well known that control of Markovian systems is a difficult problem. This paper considers synchronization control of Markovian coupled nonlinear systems with random delays. A new control scheme is proposed. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained such that the coupled system can be asymptotically synchronized onto an isolated system. The synchronization criteria include classical mode-dependent and mode-independent results as special cases. The design method of the control gains is also given. Compared with mode-dependent and mode-independent control methods, our results are more practical and have lower conservatism, respectively. Numerical simulations are given to verify the effectiveness of the theoretical results.     

Input-to-state stability of impulsive inertial memristive neural networks with time-varying delayed

The property of input-to-state stability (ISS) of inertial memristor-based neural networks with impulsive effects is studied. Firstly, according to the characteristics of memristor and inertial neural networks, the inertial memristor-based neural networks are built. Secondly, based on the impulsive control theory, the average impulsive interval approach, Halanay differential inequality, Lyapunov method and comparison property, some sufficient conditions ensuring ISS of the inertial memristor-based neural networks under impulsive controller are derived. In this paper, we consider two types of impulse, stabilizing impulses and destabilizing impulses. When the inertial memristor-based neural networks are originally not ISS, by choosing a suitable lower bound of the average impulsive interval, the stabilizing impulses can be used to stabilize the inertial memristor-based neural networks. On the contrary, the inertial memristor-based neural networks are originally ISS, by restricting the upper bound of the average impulsive interval, the ISS of inertial memristor-based neural networks with destabilizing impulses can be ensured. Finally, numerical results are presented to illustrate the main results.     

Further mean-square asymptotic stability of impulsive discrete-time stochastic BAM neural networks with Markovian jumping and multiple time-varying delays

In this paper, the asymptotic stability analysis is investigated for a kind of discrete-time bidirectional associative memory (BAM) neural networks with the existence of perturbations namely, stochastic, Markovian jumping and impulses. Based on the theory of stability, a novel Lyapunov–Krasovskii function is constructed and by utilizing the concept of delay partitioning approach, a new linear-matrix-inequality (LMI) based criterion for the stability of such a system is proposed. Furthermore, the derived sufficient conditions are expressed in the structure of LMI, which can be easily verified by a known software package that guarantees the globally asymptotic stability of the equilibrium point. Eventually, a numerical example with simulation is given to demonstrate the effectiveness and applicability of the proposed method.     

Stability and synchronization criteria for fractional order competitive neural networks with time delays: An asymptotic expansion of Mittag Leffler function

Competitive neural networks(CNNs) has not been well developed in nonlinear fractional order dynamical system, which is developed first time in this paper. Then, by means of a proper Lyapunov functional, asymptotic expansion of Mittag-Leffler function properties, together with some Caputo derivative properties, the testable novel sufficient conditions are given to guarantee the existence, uniqueness of the equilibrium point as well as global asymptotic stability for a class of fractional order competitive neural networks (FOCNNs) are all derived in the form of matrix elements. Furthermore, the boundedness for the solution of FOCNN is presented by employing Cauchy–Schwartz inequality and Gronwall inequality. Besides, a linear feedback control and adaptive feedback control are designed to achieve the global asymptotic synchronization criterion for FOCNNs with time delay and these explored consequences are extended from some previous integer order CNNs output. At last, two numerical simulations are performed to illustrate the effectiveness of our proposed theoretical results.     

Event-triggered synchronization of delayed neural networks with actuator saturation using quantized measurements

This paper studies event-triggered synchronization control problem for delayed neural networks with quantization and actuator saturation. Firstly, in order to reduce the load of network meanwhile retain required performance of system, the event-triggered scheme is adopted to determine if the sampled signal will be transmitted to the quantizer. Secondly, a synchronization error model is constructed to describe the master-slave synchronization system with event-triggered scheme, quantization and input saturation in a unified framework. Thirdly, on the basis of Lyapunov–Krasovskii functional, sufficient conditions for stabilization are derived which can ensure synchronization of the master system and slave system; particularly, a co-designed parameters of controller and the corresponding event-triggered parameters are obtained under the above stability condition. Lastly, two numerical examples are employed to illustrate the effectiveness of the proposed approach.     

Finite-time stabilization of memristor-based inertial neural networks with discontinuous activations and distributed delays

In this paper, the finite-time stabilization problem for memristor-based inertial neural networks (MINNs) with discontinuous activations (DAs) and distributed delays is investigated. To deal with the discontinuous property of the MINNs, the nonsmooth analysis theory is invoked. Furthermore, to simplify the MINNs with second-order state derivative, an order-reduced method is adopted. Then the second-order MINNs is transformed into a simpler first-order differential system. Moreover, the verifiable algebraic criteria are derived for the finite-time stabilization of MINNs with DAs and distributed delays under the designed control approach. Finally, the effectiveness of the obtained results are illustrated via numerical simulations.     

Design of memory controllers for finite-time stabilization of delayed neural networks with uncertainty

In this paper, we investigate the problem of finite-time stabilization of time-varying delayed neural networks with uncertainty. By employing the Lyapunov approach and linear matrix inequalities (LMIs), two different memory controllers are derived to achieve the finite-time stabilization of the addressed neural networks. Moreover, the upper bound of the setting-time for stabilization can be estimated via different Lyapunov functions. Our results improve and extend some recent works. Finally, the effectiveness and feasibility of the proposed controllers are demonstrated by numerical simulations.     

Composite anti-disturbance control for uncertain Markovian jump systems with actuator saturation based disturbance observer and adaptive neural network

This paper studies the problem of composite control for a class of uncertain Markovian jump systems (MJSs) with partial known transition rates, multiple disturbances and actuator saturation. Compared with the existing results, a novel robust composite control scheme is put forward by virtue of adaptive neural network technique. For MJSs, the partial unknown information on transition rates and the actuator saturation influence the design of disturbance observer and the robust H_∞ controller. Firstly, without taking account of external disturbances, the network reconstruction error and saturation, a novel robust adaptive control strategy is established to ensure that all the signals of the closed-loop system are asymptotically bounded in mean square. Secondly, the solvability condition for ensuring the robust H_∞ performance is given by using a modified adaptive law, where the saturation is treated as a disturbance-like signal. Finally, the simulations for a numerical example and an application example are performed to validate the effectiveness of the proposed results.     

Complex dynamics and stability analysis in a discrete hybrid bioeconomic system with double time delays

In this paper, a discrete hybrid three-species food chain system is proposed, where commercial harvesting on top predator is considered. Two time delays are introduced to represent gestation delay for prey and predator population, respectively. In absence of time delay, sufficient conditions associated with economic interest and step size are derived to show system undergoes flip bifurcation. In presence of double time delays, existence of Neimark–Sacker bifurcation and local stability switch are discussed due to variations of time delays. Furthermore, by utilizing new normal form of delayed discrete hybrid system and center manifold theorem, direction and stability of Neimark–Sacker bifurcation are studied. Numerical simulations are performed not only to validate theoretical analysis, but also exhibit cascades of period-doubling bifurcation, chaotic behavior and stable closed invariant curve.     

New stability and stabilization conditions for stochastic neural networks of neutral type with Markovian jumping parameters

This paper discusses the stabilization criteria for stochastic neural networks of neutral type with both Markovian jump parameters. First, delay-dependent conditions to guarantee the globally exponential stability in mean square and almost surely exponential stability of such systems are obtained by combining an appropriate constructed Lyapunov–Krasovskii functional with the semi-martingale convergence theorem. These conditions are in terms of the linear matrix inequalities (LMIs), which can be some less conservative than some existing results. Second, based on the obtained stability conditions, the state feedback controller is designed. Finally, four numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.     

Extended dissipative analysis for aircraft flight control systems with random nonlinear actuator fault via non-fragile sampled-data control

This paper addresses the issue of reliable feedback control of an uncertain aircraft flight control systems with disturbances via non-fragile sampled-data control approach. In particular, the parameter uncertainties are assumed to be randomly occurring which is described by the Bernoulli distributed sequences. By constructing a suitable Lyapunov–Krasovskii functional together with Wirtinger-based inequality, a new set of sufficient conditions in terms of linear matrix inequalities is obtained to ensure the asymptotic stability and extended dissipativity of the aircraft flight control systems not only when all actuators are operational, but also in case of some actuator failures. Finally, simulation results are conducted to validate the effectiveness of the proposed control design technique.     

Graph theory-based finite-time synchronization of fractional-order complex dynamical networks

This paper considers the finite-time synchronization problem for a class of fractional-order complex dynamical networks (FOCDNs). By utilizing the properties of fractional calculus and fractional-order comparison principle, we propose a new lemma. Base on the new lemma, some analysis techniques and algebraic graph theory method, some novel criteria are given to ensure finite-time synchronization of FOCDNs, and the upper bound of the setting time for synchronization is estimated. At last, numerical simulations are given to verify the effectiveness of the obtained results.     

Event-triggered dissipative state estimation for Markov jump neural networks with random uncertainties

This paper is concerned with the problem of event-triggered dissipative state estimation for Markov jump neural networks with random uncertainties. The event-triggered mechanism is introduced to save the limited communication bandwidth resource and preserve the desired system performance. The phenomenon of randomly occurring parameter uncertainties is considered to increase utilizability of the proposed method. To describe such a randomly occurring phenomenon, some mutually independent Bernoulli distributed white sequences are adopted. A mode-dependent state estimator is designed in this paper, which ensures that the estimation error system is extended stochastically dissipative. By using the Lyapunov–Krasovskii functional approach and an optimized decoupling approach, an expected state estimator can be built by solving some sufficient conditions. Two numerical examples are presented to demonstrate the correctness and effectiveness of the proposed method.     

Optimal jamming attack schedule for remote state estimation with two sensors

In cyber-physical systems (CPS), cyber threats emerge in many ways which can cause significant destruction to the system operation. In wireless CPS, adversaries can block the communications of useful information by channel jamming, incurring the so-called denial of service (DoS) attacks. In this paper, we investigate the problem of optimal jamming attack scheduling against remote state estimation wireless network. Specifically, we consider that two wireless sensors report data to a remote estimator through two wireless communication channels lying in two unoverlapping frequency bands, respectively. Meanwhile, an adversary can select one and only one channel at a time to execute jamming attack. We prove that the optimal attack schedule is continuously launching attack on one channel determined based on the system dynamics matrix. The theoretical results are validated by numerical simulations.