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In this article, the dynamic output‐feedback H∞ control problem is investigated for discrete‐time state‐delay systems subject to exogenous disturbances and actuator saturations under the round‐robin communication protocol. Using the switched system approach, the Lyapunov–Krasovskii functional and the modified sector condition, sufficient conditions are first obtained under which the closed‐loop systems can achieve some desirable performance indices such as the boundedness, the H∞ performance and the stability in the absence of disturbances. Then, the controller is explicitly characterized by means of the solvability of linear matrix inequalities. For the case without time delays, the corresponding conditions are also presented. Subsequently, the optimization problems about the performance indices are discussed. Finally, the benefit and effectiveness of the proposed results are specifically illustrated via two simulation examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the stabilization of the T-S fuzzy fractional rectangular descriptor time-delay system. To convert the fuzzy rectangular time-delay system into the fuzzy square time-delay system, a suitable dynamic compensator of proportional and derivative type is constructed, and the admissibility of the resultant square closed-loop system is enough to guarantee the stabilization of the nonlinear rectangular descriptor time-delay system. A sufficient condition is derived to ensure the stabilization for the considered system and the dynamic compensator parameters can be computed by solving the corresponding linear matrix inequalities (LMIs). A numerical example is provided to manifest the theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the problem of containment control for a class of nonlinear multi-agent system. The local dynamics under consideration is governed by a nonlinear system with time delays and white Gaussian noise. The multi-agent system consists of both leaders and followers, and the containment control protocol proposed is an interaction between the leaders and followers characterised by time-varying delays and switching topology. Under a certain assumption on the connectivity of the whole network, by constructing a Lyapunov–Krasovskii functional, and using the average dwell time approach and some new analytical techniques, the sufficient conditions are established to ensure that each follower converges in mean square to the convex hull spanned by the leaders. A numerical example is presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the dynamic self‐triggered output‐feedback control problem is investigated for a class of nonlinear stochastic systems with time delays. To reduce the network resource consumption, the dynamic event‐triggered mechanism is implemented in the sensor‐to‐controller channel. Criteria are first established for the closed‐loop system to be stochastically input‐to‐state stable under the event‐triggered mechanism. Furthermore, sufficient conditions are given under which the closed‐loop system with dynamic event‐triggered mechanism is almost surely stable, and the output‐feedback controller as well as the dynamic event‐triggered mechanism are co‐designed. Moreover, a dynamic self‐triggered mechanism is proposed such that the nonlinear stochastic system with the designed output‐feedback controller is stochastically input‐to‐state stable and the Zeno phenomenon is excluded. Finally, a numerical example is provided to illustrate the effectiveness of proposed dynamic self‐triggered output‐feedback control scheme. [ABSTRACT FROM AUTHOR]

Summary: In this article, the nonfragile H∞ filtering problem is investigated for a class of discrete multirate time‐delayed systems over sensor networks. The probabilistic packet dropout occurs during the information transmissions among the sensor nodes in the sensor network characterized by the Gilbert‐Elliott model. In order to take the multirate sampling into account, the state updating period of the system and the sampling period of the sensors are allowed to be different. The variation of the filter gain is considered to reflect the physical errors with the filter implementation. The aim of this article is to design a set of nonfragile filters such that, in the presence of multirate sampling, time‐delays, and packet dropouts, the filtering error dynamics is exponentially mean‐square stable and also satisfies the H∞ performance requirement. By using the Lyapunov‐Krasovskii functional approach, a sufficient condition is derived, which ensures the exponential mean‐square stability and the H∞ performance requirement of the filtering error dynamics. Then, the filter gains are characterized in terms of the solution to a set of matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed filtering scheme. [ABSTRACT FROM AUTHOR]

The problem of non‐fragile extended dissipative control design for a class of generalized neural networks (GNNs) with interval time‐delay signals is investigated in this paper. By constructing a suitable Lyapunov‐Krasovskii functional (LKF) with double and triple integral terms, and estimating their derivative by using the Wirtinger single integral inequality (WSII) and Wirtinger double integral inequality (WDII) technique respectively, and that is mixed with the reciprocally convex combination (RCC) approach. A new delay‐dependent non‐fragile extended dissipative control design for GNNs are expressed in terms of the linear matrix inequalities (LMIs). Then, the desired non‐fragile extended dissipative controller can be obtained by solving the linear matrix inequalities (LMIs). Furthermore, a non‐fragile state feedback controller is designed for GNNs such that the closed‐loop system is extended dissiptive. Thus, the non‐fragile extended dissipative controller can be adopted to deal with the non‐fragile L2−L∞ performance, non‐fragile H∞ performance, non‐fragile passive performance, non‐fragile mixed H∞ and passivity performance, and non‐fragile dissipative performance for GNNs by selecting the weighting matrices. Finally, simulation studies are demonstrated for showing the feasibility of the proposed method. Among them, one example was supported by the real‐life application of the quadruple tank process system. [ABSTRACT FROM AUTHOR]

In this paper, finite‐time synchronization for a class of complex‐valued neural networks with time delays and discontinuous activations is concerned under the framework of Filippov solutions. Both state feedback and adaptive controllers are designed to overcome the difficulties in dealing with the time delay and the uncertainties of Filippov solutions. Based on the concept of Filippov solutions, differential inclusion and structuring suitable Lyapunov‐Krasovskii functionals, some sufficient conditions are obtained to guarantee that a controlled response system is synchronized with a driving system in a finite time. Finally, numerical simulations are given to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This paper aims to investigate the exponential leader‐following consensus for nonlinear multi‐agent systems with time‐varying communication and input delays by using hybrid control. Based on the Lyapunov functional method, impulsive differential equation theory and matrix analysis, we show that all the followers can achieve leader‐following consensus with the virtual leader exponentially even if only a fraction of followers can obtain the leader's information. Two classes of exponential consensus criteria as well as the convergence rates for the controlled multi‐agent systems are presented under very relaxed interaction topology conditions, i.e., the directed interaction topology among the followers is only required to have p(p>1) disjoint strong components. Finally, two numerical examples are given to validate the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper discusses the synchronization of fractional order complex valued neural networks (FOCVNN) at the presence of time delay. Synchronization criterions are achieved through the employment of a linear feedback control and comparison theorem of fractional order linear systems with delay. Feasibility and effectiveness of the proposed system are validated through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the exponential stabilization problem is discussed for nonlinear switched systems subject to the distributed time-delay. Attention is focused on the design of a state feedback controller such that, the closed-loop system is exponentially stable with a guaranteed weighted L 2 gain. By resorting to the average dwell time method and the piecewise Lyapunov functional approach, sufficient conditions are derived for the solvability of the addressed problem in terms of the feasibility of certain Hamilton–Jacobi inequalities (HJIs). The explicit expression of the desired controller is formulated via solving the presented set of HJIs. Furthermore, within the proposed framework, the exponential stabilization problems are investigated, respectively, for nonlinear switched systems with mixed time-delays and linear switched systems with the distributed time-delay. Finally, a simulation example is given to illustrate the effectiveness and applicability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the security-guaranteed filtering problem is studied for a class of nonlinear stochastic discrete time-delay systems with randomly occurring sensor saturations (ROSSs) and randomly occurring deception attacks (RODAs). The nonlinearities in systems satisfy the sector-bounded conditions, and the time-varying delays are unknown with given lower and upper bounds. A novel measurement output model is proposed to reflect both the ROSSs and the RODAs. A new definition is put forward on the security level with respect to the noise intensity, the energy bound of the false signals, the energy of the initial system state, and the desired security degree. We aim at designing a filter such that, in the presence of ROSSs and RODAs, the filtering error dynamics achieves the prescribed level of security. By using the stochastic analysis techniques, a sufficient condition is first derived under which the filtering error system is guaranteed to have the desired security level, and then, the filter gain is designed by solving a linear matrix inequality with nonlinear constraints. Finally, a numerical example is provided to demonstrate the feasibility of the proposed filtering scheme. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the robustfiltering problem for a class of nonlinear discrete time-delay stochastic systems. The system under consideration involves parameter uncertainties, stochastic disturbances, time-varying delays and sector nonlinearities. Both missing measurements and randomly occurring nonlinearities are described via the binary switching sequences satisfying a conditional probability distribution, and the nonlinearities are assumed to be sector bounded. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time-delays, the dynamics of the filtering error is constrained to be robustly exponentially stable in the mean square, and a prescribeddisturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality. Finally, a numerical example is exploited to show the usefulness of the results derived. [ABSTRACT FROM AUTHOR]

We examine the stability problem for delayed neutral-type neural networks (NNs) with interval time-varying delay signals under the effects of leakage term by constructing a suitable Lyapunov–Krasovskii functionals (LKFs) with the triple- and four-integral terms and using the famous Jensen inequality, Wirtinger single integral inequality (WSII), and Wirtinger double integral inequality (WDII), combined with the reciprocally convex approach (RCC) for the stability of addressing NNs. Therefore, the major contribution of this study lies in a consideration of new integral inequalities and improved LKFs, fully taking the relationship between the terms in the Leibniz–Newton formula within the framework of linear matrix inequalities (LMIs). Moreover, we assume that the lower bound of interval time-varying delay is not restricted to zero. Using several examples, we show that the proposed stability criterion is less conservative than previous results. Also, the proposed technique is applied to benchmark problem that is associated with reasonable issues to showing feasibility on a real-world problem, including transporting time delay signals and leakage delay as a process variable in the quadruple-tank process system. [ABSTRACT FROM AUTHOR]

This paper is concerned with the event-triggered H ∞ fusion estimation problem for uncertain discrete-time Hamiltonian systems with time-varying delays and sensor saturations. In order to improve the efficiency of resource utilization, a component-based event-triggered mechanism is implemented on the communication path from sensors to the estimator, where each output is sent only when a prescribed event-triggering condition is satisfied. By considering the structural characteristics of discrete-time Hamiltonian systems and utilizing the Lyapunov–Krasovskii stability, sufficient conditions are established to guarantee the augmented system (i.e., the underlying system combined with the estimation error dynamics) is locally exponentially stable. Meanwhile, the estimator gain is acquired by resorting the approach of certain matrix inequality. Finally, two examples are provided to demonstrate the effectiveness of the proposed scheme. • The event-triggered fusion estimation problem is considered. • Uncertain discrete-time Hamiltonian systems are dealt with. • Both time-varying delays and sensor saturations are investigated. • A component-based event-triggered mechanism is implemented. • Sufficient conditions are established for the stability of the estimation errors. [ABSTRACT FROM AUTHOR]

Abstract This paper focus on the synchronization of complex-valued neural networks (CVNNs) with both discrete and distributed two additive time-varying delays. By applying matrix inequality technique and exploiting reciprocally convex approach, several delay-dependent criteria are presented in the form of linear matrix inequalities (LMIs) to ensure the global synchronization of CVNNs via structuring an appropriate Lyapunov–Krasovskii functional. An example with simulations is provided to ensure the feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

Abstract The periodicity problem of a class of Cohen–Grossberg-type fuzzy neural networks with impulses and time-varying delays is concerned in this paper. Via constructing a delay differential inequality, and applying fuzzy theory and the Lyapunov method, several criteria which ensure the existence and exponential stability of the periodic solutions for the considered systems are derived. An example is shown to illustrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the analysis problem for the globally asymptotic stability of a class of stochastic neural networks with finite or infinite distributed delays. By using the delay decomposition idea, a novel augmented Lyapunov–Krasovskii functional containing double and triple integral terms is constructed, based on which and in combination with the Jensen integral inequalities, a less conservative stability condition is established for stochastic neural networks with infinite distributed delay by means of linear matrix inequalities. As for stochastic neural networks with finite distributed delay, the Wirtinger-based integral inequality is further introduced, together with the augmented Lyapunov–Krasovskii functional, to obtain a more effective stability condition. Finally, several numerical examples demonstrate that our proposed conditions improve typical existing ones. [ABSTRACT FROM AUTHOR]

Abstract This article mainly concerns the synchronization in finite-time to the time-varying delay fractional order memristive competitive neural networks (TMFCNNs) with leakage delay. By means of Fillipov’s theory, Gronwall–Bellman integral inequality, H o ¨ lder’s inequality, and the Caputo derivative properties, the novel algebraic sufficient conditions are proposed to guarantee the synchronization in finite time of addressing TMFCNNs with non-integer order: 0 < p < 1 2 and 1 2 ≤ p < 1 via finite-time output feedback controller. Up to now, there are no relevant results in fractional order competitive-type neural networks, and this article makes filling up for this gap. The obtained results are improved to some existing results on integer-order memristive competitive neural networks. Finally, two numerical examples with simulations are also designed to confirm the merits of the proposed theoretical results, while we estimate the upper bound of the settling time for the synchronization errors. [ABSTRACT FROM AUTHOR]

In this paper, the problem on synchronization is investigated for a class of impulsive complex-valued neural networks with discrete and distributed time-varying delays as well as leakage delay. By constructing appropriate Lyapunov–Krasovskii functional, and using Newton–Leibniz formulation, inequality technique and free-weighting matrix method, several sufficient criteria to guarantee the global μ -synchronization are derived for the considered impulsive complex-valued neural networks. The provided conditions are expressed in terms of linear matrix inequalities, and are dependent on the sizes of discrete delays, distributed delays and leakage delay. An example with simulations is provided to verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, global asymptotic stability of impulsive fractional-order complex-valued neural networks with time delay is considered. By employing contraction mapping principle, comparison theorem and inequality scaling skills, several sufficient conditions to ensure the existence, uniqueness and global asymptotic stability of the equilibrium point for the considered neural networks are established. A numerical example illustrates the validity and feasibility of the obtained result. [ABSTRACT FROM AUTHOR]

In this paper, the recursive filtering is investigated for a type of time-delayed stochastic nonlinear systems with event-based communication protocols and missing measurements. A varying condition threshold in event triggering protocols is introduced to better match up with the system dynamic performance. The purpose of this paper is to develop an easy-implemented recursive algorithm with consideration of linearization errors, time-delays, packet losses as well as adopted communication protocols. By carrying out some elaborate mathematical operation, the desired parameters can be derived by means of the solutions to two Riccati-like difference equations. Such parameters can effectively suppress the trace of filtering error covariances and therefore the developed filtering algorithm is suboptimal. Finally, an illustrative example is presented to show the effectiveness of the developed filtering algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the problems of exponential stability and dissipativity of generalized neural networks (GNNs) with time-varying delay signals. By constructing a novel Lyapunov–Krasovskii functionals (LKFs) with triple integral terms that contain more advantages of the state vectors of the neural networks, and the upper bound on the time-varying delay signals are formulated. We employ a new integral inequality technique (IIT), free-matrix-based (FMB) integral inequality approach, and Wirtinger double integral inequality (WDII) technique together with the reciprocally convex combination (RCC) approach to bound the time derivative of the LKFs. An improved exponential stability and strictly ( Q , S , R ) - γ -dissipative conditions of the addressed systems are represented by the linear matrix inequalities (LMIs). Finally, four interesting numerical examples are developed to verify the usefulness of the proposed method with a practical application to a biological network. [ABSTRACT FROM AUTHOR]

This paper is concerned with the passivity problem for neural networks with leakage delay and time-varying transmission delay. Using some novel Lyapunov-Krasovskii (L-K) functionals, and combining with the Wirtinger integral inequality, some less conservative delay-dependent passivity conditions are proposed in terms of linear matrix inequalities (LMIs). Different from the existing approaches, the model transformation is abandoned in this paper, and the proposed L-K functionals incorporate the interconnected terms related to both the leakage delay and the time-varying delay. Numerical examples show that the obtained conditions are less conservative. [ABSTRACT FROM AUTHOR]

In this paper, finite-time synchronization (FTS) of memristor-based recurrent neural networks (MNNs) with time-varying delays is investigated by designing a new switching controller. First, by using the differential inclusions theory and set-valued maps, sufficient conditions to ensure FTS of MNNs are obtained under the two cases of 0 < α < 1 and α = 0 , and it is derived that α = 0 is the critical value of 0 < α < 1 . Next, it is discussed deeply on the relation between the parameter α and the synchronization time. Then, a new controller with a switching parameter α is designed which can shorten the synchronization time. Finally, some numerical simulation examples are provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates an issue of bifurcation control for a novel incommensurate fractional-order predator–prey system with time delay. Firstly, the associated characteristic equation is analyzed by taking time delay as the bifurcation parameter, and the conditions of creation for Hopf bifurcation are established. It is demonstrated that time delay can heavily effect the dynamics of the proposed system and each order has a major influence on the creation of bifurcation simultaneously. Then, a linear delayed feedback controller is introduced to successfully control the Hopf bifurcation for such system. It is shown that the control effort is markedly influenced by feedback gain. It is further found that the onset of the bifurcation can be delayed as feedback gain decreases. Finally, two illustrative examples are exploited to verify the validity of the obtained newly results. [ABSTRACT FROM AUTHOR]

In this paper, the non-fragile state estimation problem is investigated for a class of continuous neural networks with time-delays and nonlinear perturbations. The estimator to be designed is of a simple linear structure without requiring the exact information of the activation functions or the time-delays, and is therefore easy to be implemented. Furthermore, the designed estimator gains are allowed to undergo multiplicative parameter variations within a given range and the non-fragility is guaranteed against possible implementation errors. The main purpose of the addressed problem is to design a non-fragile state estimator for the recurrent delayed neural networks such that the dynamics of the estimation error converges to the equilibrium asymptotically irrespective of the admissible parameter variations with the estimator gains. By employing a combination of the Lyapunov functionals and the matrix analysis techniques, sufficient conditions are established to ensure the existence of the desired estimators and the explicit characterization of such estimators are then given via solving a linear matrix inequality. Finally, a simulation example is used to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of designing a non-fragile state estimator for a class of uncertain discrete-time neural networks with time-delays. The norm-bounded parameter uncertainties enter into all the system matrices, and the network output is of a general type that contains both linear and nonlinear parts. The additive variation of the estimator gain is taken into account that reflects the possible implementation error of the neuron state estimator. The aim of the addressed problem is to design a state estimator such that the estimation performance is non-fragile against the gain variations and also robust against the parameter uncertainties. Sufficient conditions are presented to guarantee the existence of the desired non-fragile state estimators by using the Lyapunov stability theory and the explicit expression of the desired estimators is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design approach. [ABSTRACT FROM AUTHOR]

In this paper, the non-fragile state estimation problem is investigated for a class of discrete-time neural networks subject to Markovian jumping parameters and time delays. In terms of a Markov chain, the mode switching phenomenon at different times is considered in both the parameters and the discrete delays of the neural networks. To account for the possible gain variations occurring in the implementation, the gain of the estimator is assumed to be perturbed by multiplicative norm-bounded uncertainties. We aim to design a non-fragile state estimator such that, in the presence of all admissible gain variations, the estimation error converges to zero exponentially. By adopting the Lyapunov–Krasovskii functional and the stochastic analysis theory, sufficient conditions are established to ensure the existence of the desired state estimator that guarantees the stability of the overall estimation error dynamics. The explicit expression of such estimators is parameterized by solving a convex optimization problem via the semi-definite programming method. A numerical simulation example is provided to verify the usefulness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the almost sure H ∞ sliding mode control (SMC) problem for nonlinear stochastic systems with Markovian switching and time-delays. An integral sliding surface is first constructed for the addressed system. Then, by employing the stopping time method combined with martingale inequalities, sufficient conditions are established to ensure the almost surely exponential stability and the H ∞ performance of the system dynamics in the specified sliding surface. A SMC law is designed to guarantee the reachability of the specified sliding surface almost surely. Furthermore, the obtained results are applied to a class of special nonlinear stochastic systems with Markovian switching and time-delays, where the desired SMC law is obtained in terms of the solutions to a set of matrix inequalities. Finally, a numerical example is given to show the effectiveness of the proposed SMC scheme. [ABSTRACT FROM AUTHOR]

By using exponential dichotomy theory, contraction mapping principle and discrete-continuous analysis method, we obtain some new sufficient conditions ensuring the existence and global exponential stability of the almost periodic solutions for a class of neutral-type neural networks with distributed leakage delays on time scales. An example is provided to demonstrate the usefulness of the main results obtained. [ABSTRACT FROM AUTHOR]

This brief is devoted to examine the exponential stability for highly nonlinear hybrid neutral stochastic systems with time varying delays by the novel approach of multiple degenerate functionals. The asymptotic stability criteria relying on delays sizes for nonlinear hybrid neutral stochastic systems with constant delays had already been explored. But, the existing literature required some rigorous conditions and did not take the convergent speed of stability and time varying delays into account. This brief is to relax the rigorous conditions, consider the factor of time varying delays, and investigate the exponentially convergent speed, which significantly develops the existing theory. [ABSTRACT FROM AUTHOR]