O. M. Kwon

Stability of time-delay systems via Wirtinger-based double integral inequality

Based on the Wirtinger-based integral inequality, a double integral form of the Wirtinger-based integral inequality (hereafter called as Wirtinger-based double integral inequality) is introduced in this paper. To show the effectiveness of the proposed inequality, two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities (LMIs). The advantage of employing the proposed inequalities is illustrated via two numerical examples.

LMI optimization approach on stability for delayed neural networks of neutral-type

In this paper, the global asymptotic stability of delayed cellular neural networks of neutral-type is investigated. A novel delay-dependent criterion for the stability using the Lyapunov stability theory and linear matrix inequality (LMI) framework is presented. Since the condition is dependent on the size of time delay, it is usually less conservative than delay-independent ones. Two numerical examples are given to show the effectiveness of proposed method.

A new stability criterion for bidirectional associative memory neural networks of neutral-type

In the paper, the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory (BAM) neural networks of neutral type by using the Lyapunov method. A new stability criterion is derived in terms of linear matrix inequality (LMI) to ascertain the global asymptotic stability of the BAM. The LMI can be solved easily by various convex optimization algorithms. A numerical example is illustrated to verify our result.

Further results on state estimation for neural networks of neutral-type with time-varying delay

In this paper, further result on design problem of state estimator for a class of neural networks of neutral type is presented. A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is derived. A numerical simulation is given to show the effectiveness of proposed estimator.

New approaches on stability criteria for neural networks with interval time-varying delays

Abstract This paper concerns the problem of delay-dependent stability criteria for neural networks with interval time-varying delays. First, by constructing a newly augmented Lyapunov–Krasovskii functional and combining with a reciprocally convex combination technique, less conservative stability criterion is established in terms of linear matrix inequalities (LMIs), which will be introduced in Theorem 1 . Second, by taking different interval of integral terms of Lyapunov–Krasovskii functional utilized in Theorem 1 , further improved stability criterion is proposed in Theorem 2 . Third, a novel approach which divides the bounding of activation function into two subinterval are proposed in Theorem 3 to reduce the conservatism of stability criterion. Finally, through two well-known numerical examples used in other literature, it will be shown the proposed stability criteria achieves the improvements over the existing ones and the effectiveness of the proposed idea.

Stochastic sampled-data control for state estimation of time-varying delayed neural networks

This study examines the state estimation problem for neural networks with a time-varying delay. Unlike other studies, the sampled-data with stochastic sampling is used to design the state estimator using a novel approach that divides the bounding of the activation function into two subintervals. To fully use the sawtooth structure characteristics of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. The desired estimator gain can be characterized in terms of the solution to linear matrix inequalities (LMIs). Finally, the proposed method is applied to two numerical examples to show the effectiveness of our result.

Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control

This article investigates the robust synchronisation problem for uncertain nonlinear chaotic systems. The norm-bounded uncertainties enter into the chaotic systems in random ways, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequences. For this synchronisation problem, the sampled-data controller that has randomly varying sampling intervals is considered. In order to fully use the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. By the Lyapunov stability theory and the linear matrix inequality (LMI) framework, the existence condition for the sample-date controller that guarantees the robust mean-square synchronisation of chaotic systems is derived in terms of LMIs. Finally, in order to show the effectiveness of our result, the proposed method is applied to two numerical examples: one is Chuas chaotic systems and the other is the hyperchaotic Rössler system.

Extended Dissipative Analysis for Neural Networks With Time-Varying Delays

In this brief, an extended dissipativity analysis was conducted for a neural network with time-varying delays. The concept of the extended dissipativity can be used to solve for the H∞, L2 - L∞, passive, and dissipative performance by adjusting the weighting matrices in a new performance index. In addition, the activation function dividing method is modified by introducing a tuning parameter. Examples are provided to show the effectiveness and less conservatism of the proposed method.

On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays

In this paper, we propose a new stability criterion for uncertain neutral systems. The considered system has time-varying structured uncertainties and time-varying delay. Based on the Lyapunov method, a delay-dependent criterion for asymptotic stability is derived in terms of LMI (linear matrix inequality). Numerical examples are given to show the effectiveness of our results.

State estimation for neural networks of neutral-type with interval time-varying delays

In this paper, the design problem of state estimator for a class of neural networks of neutral-type with interval time-varying delays is studied. The interval time-varying delay does not have constraint that its derivative is less than 1. The constraint is widely used to deal with time-varying delays in many papers. A delay-dependent linear matrix inequality (LMI) criterion for existence of the estimator is proposed by using Lyapunov method. The criterion can be easily solved by various convex optimization algorithms. A numerical example is given to show the effectiveness of proposed method.