A unified approach to the stability of generalized static neural networks with linear fractional uncertainties and delays

Stability and Dissipativity Analysis for Neutral Type Stochastic Markovian Jump Static Neural Networks with Time Delays

This paper studies the global asymptotic stability and dissipativity problem for a class of neutral type stochastic Markovian Jump Static Neural Networks (NTSMJSNNs) with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii Functional (LKF) with some augmented delay-dependent terms and by using integral inequalities to bound the derivative of the integral terms, some new sufficient conditions have been obtained, which ensure that the global asymptotic stability in the mean square. The results obtained in this paper are expressed in terms of Strict Linear Matrix Inequalities (LMIs), whose feasible solutions can be verified by effective MATLAB LMI control toolbox. Finally, examples and simulations are given to show the validity and advantages of the proposed results.

Reduced-Order Filtering of Delayed Static Neural Networks With Markovian Jumping Parameters

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order and filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results.

Improved Stability Analysis for Delayed Neural Networks

In this brief, by constructing an augmented Lyapunov-Krasovskii functional in a triple integral form, the stability analysis of delayed neural networks is investigated. In order to exploit more accurate bounds for the derivatives of triple integrals, new double integral inequalities are developed, which include some recently introduced estimation techniques as special cases. The information on the activation function is taken into full consideration. Taking advantages of the proposed inequalities, the stability criteria with less conservatism are derived. The improvement of the obtained approaches is verified by numerical examples.

Dynamic IQC-Based Control of Uncertain LFT Systems With Time-Varying State Delay

This paper presents a new exact-memory delay control scheme for a class of uncertain systems with time-varying state delay under the integral quadratic constraint (IQC) framework. The uncertain system is described as a linear fractional transformation model including a state-delayed linear time-invariant (LTI) system and time-varying structured uncertainties. The proposed exact-memory delay controller consists of a linear state-feedback control law and an additional term that captures the delay behavior of the plant. We first explore the delay stability and the L₂ -gain performance using dynamic IQCs incorporated with quadratic Lyapunov functions. Then, the design of exact-memory controllers that guarantee desired L₂ -gain performance is examined. The resulting delay control synthesis conditions are formulated in terms of linear matrix inequalities, which are convex on all design variables including the scaling matrices associated with the IQC multipliers. The IQC-based exact-memory control scheme provides a novel approach for delay control designs via convex optimization, and advances existing control methods in two important ways: 1) better controlled performance and 2) simplified design procedure with less computational cost. The effectiveness and advantages of the proposed approach have been demonstrated through numerical studies.

Finite-Time Consensus of Multiagent Systems With a Switching Protocol

In this paper, we study the problem of finite-time consensus of multiagent systems on a fixed directed interaction graph with a new protocol. Existing finite-time consensus protocols can be divided into two types: 1) continuous and 2) discontinuous, which were studied separately in the past. In this paper, we deal with both continuous and discontinuous protocols simultaneously, and design a centralized switching consensus protocol such that the finite-time consensus can be realized in a fast speed. The switching protocol depends on the range of the initial disagreement of the agents, for which we derive an exact bound to indicate at what time a continuous or a discontinuous protocol should be selected to use. Finally, we provide two numerical examples to illustrate the superiority of the proposed protocol and design method.

Input-Output Approach to Control for Fuzzy Markov Jump Systems With Time-Varying Delays and Uncertain Packet Dropout Rate

This paper is concerned with H∞ control problem for a class of discrete-time Takagi-Sugeno fuzzy Markov jump systems with time-varying delays under unreliable communication links. It is assumed that the data transmission between the plant and the controller are subject to randomly occurred packet dropouts satisfying Bernoulli distribution and the dropout rate is uncertain. Based on a fuzzy-basis-dependent and mode-dependent Lyapunov function, the existence conditions of the desired H∞ state-feedback controllers are derived by employing the scaled small gain theorem such that the closed-loop system is stochastically stable and achieves a guaranteed H∞ performance. The gains of the controllers are constructed by solving a set of linear matrix inequalities. Finally, a practical example of robot arm is provided to illustrate the performance of the proposed approach.

Further result on guaranteed H∞ performance state estimation of delayed static neural networks

This brief considers the guaranteed H∞ performance state estimation problem of delayed static neural networks. An Arcak-type state estimator, which is more general than the widely adopted Luenberger-type one, is chosen to tackle this issue. A delay-dependent criterion is derived under which the estimation error system is globally asymptotically stable with a prescribed H∞ performance. It is shown that the design of suitable gain matrices and the optimal performance index are accomplished by solving a convex optimization problem subject to two linear matrix inequalities. Compared with some previous results, much better performance is achieved by our approach, which is greatly benefited from introducing an additional gain matrix in the domain of activation function. An example is finally given to demonstrate the advantage of the developed result.

Improved stability criteria of static recurrent neural networks with a time-varying delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

Delay-dependent stability criteria for reaction–diffusion neural networks with time-varying delays

This paper studies the global asymptotic stability problem of a class of reaction–diffusion neural networks with time-varying delays. To overcome the difficulty caused by the partial differential term, a novel Lyapunov–Krasovskii functional is proposed, and a partial differential equation technique together with a linear operator approach are also applied to obtain the delay-dependent stability criteria, which are less conservative than the existing results. Finally, simulation examples are given to verify and illustrate the theoretical analysis.

Stability analysis of time-delay neural networks subject to stochastic perturbations

This paper is concerned with the problem of mean-square exponential stability of uncertain neural networks with time-varying delay and stochastic perturbation. Both linear and nonlinear stochastic perturbations are considered. The main features of this paper are twofold: 1) Based on generalized Finsler lemma, some improved delay-dependent stability criteria are established, which are more efficient than the existing ones in terms of less conservatism and lower computational complexity; and 2) when the nonlinear stochastic perturbation acting on the system satisfies a class of Lipschitz linear growth conditions, the restrictive condition P < δI (or the similar ones) in the existing results can be relaxed under some assumptions. The usefulness of the proposed method is demonstrated by illustrative examples.

Synchronization of Coupled Neutral-Type Neural Networks With Jumping-Mode-Dependent Discrete and Unbounded Distributed Delays

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.