New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay

Stability of Discrete Recurrent Neural Networks with Interval Delays

A global exponential stability method for a class of discrete time recurrent neural networks with interval time-varying delays and norm-bounded time-varying parameter uncertainties is developed in this paper. The method is derived based on a new Lyapunov-Krasovskii functional to exhibit the delay-range-dependent dynamics and to compensate for the enlarged time-span. In addition, it eliminates the need for over bounding and utilizes smaller number of LMI decision variables. Effective solutions to the global stability problem are provided in terms of feasibility-testing of parameterized linear matrix inequalities (LMIs). Numerical examples are presented to demonstrate the potential of the developed technique.

LMI-BASED ASYMPTOTIC STABILITY ANALYSIS OF NEURAL NETWORKS WITH TIME-VARYING DELAYS

The problem of the global asymptotic stability for a class of neural networks with time-varying delays is investigated in this paper, where the activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. By constructing suitable Lyapunov functionals and combining with linear matrix inequality (LMI) technique, new global asymptotic stability criteria about different types of time-varying delays are obtained. It is shown that the criteria can provide less conservative result than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.

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

In this paper, the robust global asymptotic stability (RGAS) of generalized static neural networks (SNNs) with linear fractional uncertainties and a constant or time-varying delay is concerned within a novel input-output framework. The activation functions in the model are assumed to satisfy a more general condition than the usually used Lipschitz-type ones. First, by four steps of technical transformations, the original generalized SNN model is equivalently converted into the interconnection of two subsystems, where the forward one is a linear time-invariant system with a constant delay while the feedback one bears the norm-bounded property. Then, based on the scaled small gain theorem, delay-dependent sufficient conditions for the RGAS of generalized SNNs are derived via combining a complete Lyapunov functional and the celebrated discretization scheme. All the results are given in terms of linear matrix inequalities so that the RGAS problem of generalized SNNs is projected into the feasibility of convex optimization problems that can be readily solved by effective numerical algorithms. The effectiveness and superiority of our results over the existing ones are demonstrated by two numerical examples.

Stability and L2 performance analysis of stochastic delayed neural networks

This brief focuses on the robust mean-square exponential stability and L(2) performance analysis for a class of uncertain time-delay neural networks perturbed by both additive and multiplicative stochastic noises. New mean-square exponential stability and L(2) performance criteria are developed based on the delay partition Lyapunov-Krasovskii functional method and generalized Finsler lemma which is applicable to stochastic systems. The analytical results are established without involving any model transformation, estimation for cross terms, additional free-weighting matrices, or tuning parameters. Numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing ones.

A new method for stability analysis of recurrent neural networks with interval time-varying delay

This brief deals with the problem of stability analysis for a class of recurrent neural networks (RNNs) with a time-varying delay in a range. Both delay-independent and delay-dependent conditions are derived. For the former, an augmented Lyapunov functional is constructed and the derivative of the state is retained. Since the obtained criterion realizes the decoupling of the Lyapunov function matrix and the coefficient matrix of the neural networks, it can be easily extended to handle neural networks with polytopic uncertainties. For the latter, a new type of delay-range-dependent condition is proposed using the free-weighting matrix technique to obtain a tighter upper bound on the derivative of the Lyapunov-Krasovskii functional. Two examples are given to illustrate the effectiveness and the reduced conservatism of the proposed results.

Modeling and stabilization of continuous-time packet-based networked control systems

In this paper, the packet-based control approach to networked control systems (NCSs) is extended to the continuous-time case with the use of a discretization technique for continuous network-induced delay. The derived approach can effectively simultaneously deal with network-induced delay, data packet dropout, and data packet disorder and leads to a novel model for NCSs. This model offers the designer the freedom of designing different controllers with respect to specific network conditions, which is distinct from previous results and ensues better system performance. By applying switched system theory, the stability criterion for the derived model is obtained, which is then used to obtain an linear matrix inequality-based stabilized controller design method for the packet-based control approach. A numerical example is also presented, which illustrates the effectiveness of the proposed packet-based control approach by comparison.