Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays

This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples.

Coexistence and local stability of multiple equilibrium points for fractional-order state-dependent switched competitive neural networks with time-varying delays

This paper investigates the coexistence and local stability of multiple equilibrium points for a class of competitive neural networks with sigmoidal activation functions and time-varying delays, in which fractional-order derivative and state-dependent switching are involved at the same time. Some novel criteria are established to ensure that such n-neuron neural networks can have [Formula: see text] total equilibrium points and [Formula: see text] locally stable equilibrium points with m₁+m₂=n, based on the fixed-point theorem, the definition of equilibrium point in the sense of Filippov, the theory of fractional-order differential equation and Lyapunov function method. The investigation implies that the competitive neural networks with switching can possess greater storage capacity than the ones without switching. Moreover, the obtained results include the multistability results of both fractional-order switched Hopfield neural networks and integer-order switched Hopfield neural networks as special cases, thus generalizing and improving some existing works. Finally, four numerical examples are presented to substantiate the effectiveness of the theoretical analysis.

Robust adaptive fault detection and diagnosis observer design for a class of nonlinear systems with uncertainty and unknown time-varying internal delay

This paper introduces a novel robust adaptive fault detection and diagnosis (FDD) observer design approach for a class of nonlinear systems with parametric uncertainty, unknown system fault and time-varying internal delays. The conditions for the existence of the proposed FDD are obtained based on the well-known Linear Matrix Inequalities (LMI) technique. Using Lyapunov stability theory, the adaptation laws for updating the observer weights and unknown faults estimation are derived based on which the convergence of the state estimation error to zero and asymptotic stability of the error dynamics are proven. Toward this, a new structural algorithm for FDD observer design is also derived based on LMIs. The performance of the proposed method is also investigated while applying to some industrial systems. Simulation results illustrate superior performance of the proposed method for the systems subject to time-varying unknown delays on states, uncertainty in nonlinear system modeling and unknown system faults.

An analysis of delay-constrained consensus-based optimal algorithms in virtual power plants

In virtual power plants (VPPs), consensus-based distributed optimal dispatch algorithms aim to collectively minimize the operating cost. As ubiquitous latency on communication networks may lead to divergence, convergence to a nonoptimal solution, or a longer convergence time, mitigating the impacts of arbitrarily large but bounded time-varying delays is significant both in theory and in practice. To modify a typical consensus-based optimal dispatch algorithm under time-varying delays, this paper designs new update rules and introduces a reduction approach to evaluate the performance of the algorithm. The results reveal that the modified algorithm can always converge to the optimal solution with a tactical initial setup in a distributed manner if the undirected interaction topology is connected and the gain parameter is sufficiently small. The analytical expression of the gain is also given. Furthermore, we show that the convergence time is determined by the maximum time delays, the number of generators, and the convergence accuracy. Several numerical simulation studies validate our theory.

H∞ filtering for nonlinearly coupled complex networks subjected to unknown varying delays and multiple fading measurements

In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on H_∞ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system's matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the H_∞ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed H_∞ filtering approach are demonstrated via a practical example.

Stochastic quasi-synchronization of heterogeneous delayed impulsive dynamical networks via single impulsive control

This paper investigates the quasi-synchronization problem of the stochastic heterogeneous complex dynamical networks with impulsive couplings and multiple time-varying delays. It is shown that this kind of dynamical networks can achieve exponential quasi-synchronization by exerting impulsive control added on only one chosen pinning node. By employing the Lyapunov stability theory, some sufficient criteria on quasi-synchronization for this dynamical network are established, revealing the relationship between the quasi-synchronization performance and the stochastic perturbations as well as the frequency and strength of impulsive coupling. Finally, some numerical examples are used to illustrate the effectiveness of the main results.

Pole assignment stabilization for a class of switched nonlinear time-varying delay systems

This paper investigates the pole assignment stabilization with memory state feedback controllers for switched nonlinear time-varying delay systems. More general time-varying delays which depend on the subsystem number are considered. Based on novel common Lyapunov functions (CLFs), the aggregation techniques, the proprieties and the Borne-Gentina criterion, new algebraic stabilization criteria are established. The proposed design can guarantee the stability of the closed-loop systems under arbitrary switching. It allows to avoid researching a common Lyapunov function (CLF), considered a difficult matter. Four illustrate examples were finally utilized to exhibit the effectiveness of the obtained results.

H∞ sliding mode control of discrete switched systems with time-varying delays

The finite-time boundedness issue for a class of discrete switched systems with time-varying delays is investigated via sliding mode control (SMC) approach. By employing the Lyapunov functional and average dwell time method, new sufficient conditions are derived to guarantee the finite-time boundedness of the dynamic system in the novel sliding surface. By solving an optimization problem, the sliding mode controller is synthesized such that the discrete reaching condition is satisfied and the chattering is reduced. A simulation example tests the feasibility of the provided SMC scheme.

Robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays via sliding mode approach

In this paper, the issue of robust observer-based H_∞ control for uncertain discrete singular systems with time-varying delays is investigated via sliding mode control (SMC). A sliding mode strategy is presented combined with the observer technique, since the system states are unmeasured. The distinguishing feature of the provided strategy is that a novel sliding surface is constructed based upon the estimated states such that the resulting full-order closed-loop system is generated. Furthermore, by employing Lyapunov-Krasovskii functional, new sufficient criteria in terms of a solvable linear matrix inequality (LMI) is derived, insuring that the closed-loop system is admissible with an H_∞-norm bound. With the solution of the LMI, a corresponding sliding mode controller is obtained for reaching motion and reducing the chattering. At last, the theoretical results are verified in numerical tests.

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

Improved results on state feedback stabilization for a networked control system with additive time-varying delay components' controller

This paper investigates the problems of stability and stabilization for a networked control system (NCS) with additive time-varying delay components' controller. Firstly, stability of a NCS with additive time-varying delays is investigated. A novel approach with free parameters is proposed. By constructing a new Lyapunov-Krasovskii functional (LKF) with two free parameters, stability criteria are obtained. The obtained stability criteria depend not only on upper bounds of delays but also free parameters. In addition, input-output method is extended to study the stability problem for the NCS. Compared with other approaches such as input-output method, the free-parameter approach is more flexible and effective in reducing the conservatism. Then, based on the stability results, a state feedback controller is designed to guarantee the asymptotically stable of the closed-loop systems. Finally, numerical examples are provided to show the effectiveness and less conservatism of the proposed results.

O(t-α)-synchronization and Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations

This paper investigates O(t^-α)-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t^-α)-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays.

Multistability and instability analysis of recurrent neural networks with time-varying delays

This paper provides new theoretical results on the multistability and instability analysis of recurrent neural networks with time-varying delays. It is shown that such n-neuronal recurrent neural networks have exactly [Formula: see text] equilibria, [Formula: see text] of which are locally exponentially stable and the others are unstable, where k₀ is a nonnegative integer such that k₀≤n. By using the combination method of two different divisions, recurrent neural networks can possess more dynamic properties. This method improves and extends the existing results in the literature. Finally, one numerical example is provided to show the superiority and effectiveness of the presented results.

Mean square consensus of leader-following multi-agent systems with measurement noises and time delays

This paper investigates the mean square consensus problem of dynamical networks of leader-following multi-agent systems with measurement noises and time-varying delays. We consider that the fixed undirected communication topologies are connected. A neighbor-based tracking algorithm together with distributed estimators are presented. Using tools of algebraic graph theory and the Gronwall-Bellman-Halanay type inequality, we establish sufficient conditions to reach consensus in mean square sense via the proposed consensus protocols. Finally, a numerical simulation is provided to demonstrate the effectiveness of the obtained theoretical result.

Complete stability of delayed recurrent neural networks with Gaussian activation functions

This paper addresses the complete stability of delayed recurrent neural networks with Gaussian activation functions. By means of the geometrical properties of Gaussian function and algebraic properties of nonsingular M-matrix, some sufficient conditions are obtained to ensure that for an n-neuron neural network, there are exactly 3^k equilibrium points with 0≤k≤n, among which 2^k and 3^k-2^k equilibrium points are locally exponentially stable and unstable, respectively. Moreover, it concludes that all the states converge to one of the equilibrium points; i.e., the neural networks are completely stable. The derived conditions herein can be easily tested. Finally, a numerical example is given to illustrate the theoretical results.

M-matrix based robust stability and stabilization for uncertain discrete-time switched TS fuzzy systems with time-varying delays

This paper provides novel sufficient conditions on robust asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy with time-varying delays. The attention is focused on developing new algebraic criteria to break with classical criteria in terms of Linear Matrix Inequalities (LMIs). Firstly, based on the M-matrix proprieties and through l1,∞ induced norms notion, new delay-dependent sufficient conditions are derived to ensure the asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy systems with time-varying delay. Secondly, these results are extended for a class of uncertain discrete-time switched fuzzy systems with time delays, modeled by difference equations. Finally, two numerical examples and practical example (a robot arm) are provided to demonstrate the advantage and the effectiveness of our results.

New passivity criteria for memristive uncertain neural networks with leakage and time-varying delays

In this paper, the problem of passivity analysis is studied for memristor-based uncertain neural networks with leakage and time-varying delays. By combining differential inclusions with set-valued maps, the system of memristive neural networks is changed into the conventional one. By adding a triple quadratic integral and relaxing the requirement for the positive definiteness of some matrices, a proper Lyapunov-Krasovskii functional is constructed. Based on the establishment of the novel Lyapunov-Krasovskii functional, the new passivity criteria are derived by mainly applying Wirtinger-based double integral inequality, S-procedure and so on. Moreover, the conservatism of passivity conditions can be reduced. Finally, four numerical examples are given to show the effectiveness and less conservatism of the proposed criteria.

Delay-dependent exponential passivity of uncertain cellular neural networks with discrete and distributed time-varying delays

This paper is concerned with the delay-dependent exponential passivity analysis issue for uncertain cellular neural networks with discrete and distributed time-varying delays. By decomposing the delay interval into multiple equidistant subintervals and multiple nonuniform subintervals, a suitable augmented Lyapunov-Krasovskii functionals are constructed on these intervals. A set of novel sufficient conditions are obtained to guarantee the exponential passivity analysis issue for the considered system. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed results.

Further results on global state feedback stabilization of high-order nonlinear systems with time-varying delays

This paper considers the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. Comparing with the existing relevant literature, the systems under investigation allow more uncertainties, to which the existing control methods are inapplicable. By introducing sign function and necessarily modifying the method of adding a power integrator, a state feedback controller is successfully constructed to preserve the equilibrium at the origin and guarantee the global asymptotic stability of the resulting closed-loop system. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed approach.

Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling

This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies.

Stability of delayed memristive neural networks with time-varying impulses

This paper addresses the stability problem on the memristive neural networks with time-varying impulses. Based on the memristor theory and neural network theory, the model of the memristor-based neural network is established. Different from the most publications on memristive networks with fixed-time impulse effects, we consider the case of time-varying impulses. Both the destabilizing and stabilizing impulses exist in the model simultaneously. Through controlling the time intervals of the stabilizing and destabilizing impulses, we ensure the effect of the impulses is stabilizing. Several sufficient conditions for the globally exponentially stability of memristive neural networks with time-varying impulses are proposed. The simulation results demonstrate the effectiveness of the theoretical results.

Improved delay-dependent stability analysis for neural networks with time-varying delays

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with time-varying delays is considered. A new class of Lyapunov functional is proposed by considering the information of neuron activation functions adequately. By using the delay-partitioning method and the reciprocally convex technique, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the derived method.

Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach

We extend the notion of Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach. Some sufficient conditions are obtained to guarantee the synchronization of the memristor-based recurrent neural networks via delay-dependent output feedback controller in terms of linear matrix inequalities (LMIs). The activation functions are assumed to be of further common descriptions, which take a broad view and recover many of those existing methods. A Lyapunov-Krasovskii functional (LKF) with triple-integral terms is addressed in this paper to condense conservatism in the synchronization of systems with additive time-varying delays. Jensen's inequality is applied in partitioning the double integral terms in the derivation of LMIs and then a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters has emerged. Meanwhile, this paper puts forward a well-organized method to manipulate such a combination by extending the lower bound lemma. The obtained conditions not only have less conservatism but also less decision variables than existing results. Finally, numerical results and its simulations are given to show the effectiveness of the proposed memristor-based synchronization control scheme.

Robust fault detection for switched positive linear systems with time-varying delays

This paper investigates the problem of robust fault detection for a class of switched positive linear systems with time-varying delays. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the positive filter such that, for model uncertainties, unknown inputs and the control inputs, the error between the residual and fault is minimized. The problem of robust fault detection is converted into a positive L1 filtering problem. Subsequently, by constructing an appropriate multiple co-positive type Lyapunov-Krasovskii functional, as well as using the average dwell time approach, sufficient conditions for the solvability of this problem are established in terms of linear matrix inequalities (LMIs). Two illustrative examples are provided to show the effectiveness and applicability of the proposed results.

Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay

This paper investigates a class of delayed cellular neural networks (DCNN) with time-varying delay. Based on the Lyapunov-Krasovski functional and integral inequality approach (IIA), a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Unlike previous methods, the upper bound of the delay derivative is taken into consideration, even if larger than or equal to 1. It is proven that results obtained are less conservative than existing ones. Four numerical examples illustrate efficacy of the proposed methods.