Delay-dependent Asymptotic Stability Research Articles

A new LMI condition for delay-dependent asymptotic stability of delayed Hopfield neural networks

In this paper, a new delay-dependent asymptotic stability condition for delayed Hopfield neural networks is given in terms of a linear matrix inequality, which is less conservative than existing ones in the literature. This condition guarantees the existence of a unique equilibrium point and its global asymptotic stability of a given delayed Hopfield neural network. Examples are provided to show the reduced conservatism of the proposed condition.

A delay-dependent asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays

Based on the Lyapunov functional stability analysis for differential equations and the linear matrix inequality (LMI) optimization approach, A novel criterion for the global asymptotic stability of cellular neural networks with time-varying discrete and distributed delays is derived to guarantee global asymptotic stability. The criterion is expressed in terms of LMIs, which can be solved easily by various convex optimization algorithms. Some numerical examples are given to show the effectiveness of proposed method.

Delay-dependent asymptotic stability for neural networks with distributed delays

In this paper, dynamical behavior of a class of neural networks with distributed delays is studied by employing suitable Lyapunov functionals, delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural networks. Our results are applied to classical Hopfield neural networks with distributed delays and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature.

Delay-dependent asymptotic stability for neural networks with time-varying delays

We study the dynamical behavior of a class of neural network models with time-varying delays. By constructing suitable Lyapunov functionals, we obtain sufficient delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural network. Our results are applied to a two-neuron system with delayed connections between neurons, and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.

Delay-dependent asymptotic stability of a two-neuron system with different time delays

Abstract In this paper, we consider a two-neuron system with time-delayed connections between neurons. Based on the construction of Lyapunov functionals, we obtain sufficient criteria to ensure local and global asymptotic stability of the equilibrium of the neural network. The obtained conditions are shown to be less conservative and restrictive than those reported in the literature. Some examples are included to illustrate our results.

Robust stability analysis of singular linear system with delay and parameter uncertainty

This paper deals with the problem of robust stability for continuous-time singular systems with state delay and parameter uncertainty. The uncertain singular systems with delay considered in this paper are assumed to be regular and impulse free. By decomposing the systems into slow and fast subsystems,a robust delay-dependent asymptotic stability criteria based on linear matrix inequality is proposed, which is derived by using Lyapunov-Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay-dependent result. The robust delay-dependent stability criterion proposed in this paper is a sufficient condition. Finally, numerical examples and Matlab simulation are provided to illustrate the effectiveness of the proposed method.

Simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems

Simplified delay-dependent asymptotic stability conditions are provided for time-delay systems in terms of linear matrix inequalities. The redundant variables in the previous results derived by the so-called ‘descriptor system approach’ together with recently proposed bounding techniques are removed. Thus, the newly proposed conditions are equivalent to these obtained by the descriptor system approach but with reduced complexity. It is shown that the bounding technique does not have to be used in the derivation of our results. By the proposed method, delay-dependent results on H∞ performance analysis for time delay systems are also presented.

Further results on delay-dependent robust stability conditions of uncertain neutral systems

This paper deals with the problem of robust stability analysis for uncertain neutral systems. In terms of a linear matrix inequality (LMI), an improved delay-dependent asymptotic stability criterion is developed without using bounding techniques on the related cross product terms. Based on this, a new delay-dependent LMI condition for robust stability is obtained. Numerical examples are provided to show that the proposed results significantly improve the allowed upper bounds of the delay size over some existing ones in the literature. Copyright © 2005 John Wiley & Sons, Ltd.

An Analysis of Delay-Dependent Stability for Ordinary and Partial Differential Equations with Fixed and Distributed Delays

This paper is concerned with the study of the stability of ordinary and partial differential equations with both fixed and distributed delays, and with the study of the stability of discretizations of such differential equations. We start with a delay-dependent asymptotic stability analysis of scalar ordinary differential equations with real coefficients. We study the exact stability region of the continuous problem as a function of the parameters of the model. Next, it is proved that a time discretization based on the trapezium rule can preserve the asymptotic stability for the considered set of test problems. In the second part of the paper, we study delay partial differential equations. The stability region of the fully continuous problem is analyzed first. Then a semidiscretization in space is applied. It is shown that the spatial discretization leads to a reduction of the stability region when the standard second-order central difference operator is employed to approximate the diffusion operator. Finally we consider the delay-dependent stability of the fully discrete problem, where the partial differential equation is discretized both in space and in time. Some numerical examples and further discussions are given.

On Closed-Loop Stability for Mechanical Systems with Input Delays

This paper focuses on some closed-loop delay-dependent asymptotic stability problems for a large class of nonlinear underactuated mechanical systems subject to delayed inputs. Upper bounds on the delays size such that the closed-loop system stability is guaranteed are obtained in terms of some matrix inequalities. Using a time-domain approach, we show how to compute quadratic Liapunov functionals and functions for the corresponding analysis.

Mixed Delay-Independent / Delay-Dependent Stability of Linear Systems With Delayed State: An L.M.I. Approach

This paper focuses on some delay-independent / delay-dependent asymptotic stability problems of a class of linear systems described by delay-differential equations involving several constant (or time-varying) delays. We give sufficient conditions (expressed in terms of LMIs) for characterizing unbounded stability regions in the delays parameter space. Note that the presented results allow to recover previous sufficient delay-independent or delay-dependent conditions from the control literature.