Ho Y. Jung

A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays

This paper is concerned with the stability analysis of neutral type neural networks with discrete and distributed delays. Some improved delay-dependent stability results are established by using a delay partitioning approach for the networks. By employing a new type of Lyapunov-Krasovskii functionals, new delay-dependent stability criteria are derived. All the criteria are expressed in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using standard convex optimization algorithms. Finally, numerical examples are given to illustrate the less conservatism of the proposed method.

Design of state estimator for neural networks with leakage, discrete and distributed delays ☆

Abstract In this paper, the design problem of state estimator for neural networks with mixed time-varying delays and leakage delays has been investigated. By using appropriate model transformation that shifts the considered systems into the neutral-type time-delay systems, adapting a new Lyapunov–Krasovskii functional which takes into account the range of time-delay, and by making use of some inequality techniques, delay-dependent criteria are developed to estimate the neuron states through available output measurements such that the estimation error system is globally asymptotically stable. The criteria are formulated in terms of a set of linear matrix inequalities (LMIs), which can be checked efficiently by use of some standard numerical packages. Finally, three numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the presented results.

Decentralized guaranteed cost dynamic control for synchronization of a complex dynamical network with randomly switching topology

This paper considers synchronization problem of a complex dynamical network. For this problem, a decentralized guaranteed cost dynamic feedback controller is designed to achieve the synchronization of the network. Based on Lyapunov stability theory and linear matrix inequality framework, the existence condition for feasible controllers is derived in terms of linear matrix inequalities. Finally, the proposed method is applied to two numerical examples in order to show the effectiveness of our result.

Design of state estimator for genetic regulatory networks with time-varying delays and randomly occurring uncertainties ☆

In this paper, the design problem of state estimator for genetic regulatory networks with time delays and randomly occurring uncertainties has been addressed by a delay decomposition approach. The norm-bounded uncertainties enter into the genetic regulatory networks (GRNs) in random ways, and such randomly occurring uncertainties (ROUs) obey certain mutually uncorrelated Bernoulli distributed white noise sequences. Under these circumstances, the state estimator is designed to estimate the true concentration of the mRNA and the protein of the uncertain GRNs. Delay-dependent stability criteria are obtained in terms of linear matrix inequalities by constructing a Lyapunov-Krasovskii functional and using some inequality techniques (LMIs). Then, the desired state estimator, which can ensure the estimation error dynamics to be globally asymptotically robustly stochastically stable, is designed from the solutions of LMIs. Finally, a numerical example is provided to demonstrate the feasibility of the proposed estimation schemes.

Effects of leakage time-varying delays in Markovian jump neural networks with impulse control

In this paper, the stability analysis problem is investigated for delayed neural networks with mixed time-varying delays, impulsive control and Markovian jumping parameters. The mixed time-varying delays include leakage, discrete and distributed time-varying delays. Sufficient conditions for the global exponential stability in the mean square are derived by using Lyapunov-Krasovskii functional having triple integral terms and model transformation technique. The stability criterion that depends on the upper bounds of the leakage time-varying delay and its derivative is given in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical softwares. Finally, three numerical examples and simulations are given to demonstrate the usefulness and effectiveness of the presented results.

Decentralized dynamic output feedback controller design for guaranteed cost stabilization of large-scale discrete-delay systems

In this paper, we discuss how to solve dynamic output feedback controller design problem for decentralized guaranteed cost stabilization of large-scale discrete-delay system by convex optimization. Based on Lyapunov second method, an linear matrix inequality optimization problem is formulated to design the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function. A numerical example is given to illustrate the proposed method.

On the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays

In this article, the nonfragile guaranteed cost control problem is studied for a class of uncertain dynamic systems with multiple time delays and controller gain variation. The multiple time-varying delays are considered. The uncertainty is nonlinear time-varying and is bounded in magnitude. For all admissible uncertainties, time delays, and controller gain variations, the problem is to design a memoryless state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound of a given cost function. Several criteria for the existence of such controllers are derived using the Lyapunov method. A feature of the proposed method is that an upper bound on the guaranteed cost is minimized by solving a convex optimization problem with linear matrix inequalities. A numerical example is given to illustrate the proposed method.

Existence and controllability results for second-order impulsive stochastic evolution systems with state-dependent delay

In this paper, we discuss a kind of impulsive second-order stochastic evolution systems with state-dependent delay in a real separable Hilbert space. The results concerning the existence and controllability of mild solutions have been addressed. By means of the fixed point techniques, some sufficient conditions are formulated, as well as an application involving partial differential equation with impulses is presented.

Robust Delay-Dependent Stability Criteria for Dynamic Systems with Nonlinear Perturbations and Leakage Delay

This paper studies the global asymptotic stability for uncertain systems with mixed delays. The mixed delays include constant delay in the leakage term (i.e., leakage delay) and time-varying delays. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. Based on a appropriate Lyapunov–Krasovskii functional with triple integral terms, some integral inequalities and convex combination technique, a novel delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Finally, three numerical examples are included to show the superiority of the proposed method.

Non-fragile Observer-Based H ∞ Control for Discrete-Time Systems Using Passivity Theory

In this paper, non-fragile observer-based