Asymptotic stability of differential systems of neutral type

We offer sufficient conditions for the asymptotic stability of the equilibrium point of linear neutral differential systems. An application of our results to a family of artificial neural networks of neutral type is also illustrated.     

The stability of nonlinear neutral differential systems

In this paper, the author uses the method of inequality analysis to study the stability of nonlinear neutral differential systems. Some criteria for being exponentially stable in the large inC ₁ space are obtained.     

Asymptotic stability of neutral differential systems with many delays

We are concerned with delay-independent asymptotic stability of linear system of neutral differential equations. We first establish a sufficient and necessary condition for the system to be delay-independently asymptotically stable, and then give some equivalent stability conditions. This paper improves many recent results on the asymptotic stability in the literature. One example is given to show that the sufficient and necessary condition is easy to verify.     

Asymptotic stability of nonlinear systems with unbounded delays

Some asymptotic stability criteria are derived for systems of nonlinear functional differential equations with unbounded delays. The criteria are described as matrix equations or matrix inequalities, which are computationally flexible and efficient. The theories are then applied to the stabilization of time-delay systems via standard feedback control (SFC) or time-delayed feedback control (DFC). Several examples are given to illustrate the results.     

Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with infinite delay

In this article, we investigate the existence and asymptotic stability in p-th moment of a mild solution to a class of neutral stochastic integro-differential equation of fractional order involving non-instantaneous impulses with infinite delay in a Hilbert space. A new set of sufficient conditions proving existence and asymptotic stability of mild solution is derived by utilizing solution operator, functional analysis, stochastic analysis and fixed point technique. Finally, an example is provided to illustrate the obtained abstract result.     

一类广义系统的渐近稳定性

Abstract. This paper is mainly used to determine the asymptotic stability of a class of nonlineargeneralized systems through its slow subsystems under the assumption of regularity. One exam-ple is given.     

Novel delay-dependent asymptotical stability of neutral systems with nonlinear perturbations

This paper address the asymptotical stability of neutral systems with nonlinear perturbations. Some novel delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs). The resulting delay-dependent stability criteria are less conservative than the previous ones, owing to the introduction of free-weighting matrices, based on a class of novel augment Lyapunov functionals. Numerical examples are given to demonstrate that the derived conditions are much less conservative than those given in the literature.     

Absolute stability criteria for a class of nonlinear singular systems with time delay

This paper deals with the problem of absolute stability for a class of time-delay singular systems with sector-bounded nonlinearity. Both delay-independent and delay-dependent criteria are presented and formulated in the form of linear matrix inequalities (LMIs). Neither model transformation nor a bounding technique for cross-terms, nor a slack variable method is involved in obtaining the stability criteria. Numerical examples are given to show the effectiveness and improvements over some existing results.     

Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations

Summary. We consider systems of delay differential equations (DDEs) of the form with the initial condition . Recently, Torelli [10] introduced a concept of stability for numerical methods applied to dissipative nonlinear systems of DDEs (in some inner product norm), namely RN-stability, which is the straighforward generalization of the wellknown concept of BN-stability of numerical methods with respect to dissipative systems of ODEs. Dissipativity means that the solutions and corresponding to different initial functions and , respectively, satisfy the inequality , and is guaranteed by suitable conditions on the Lipschitz constants of the right-hand side function . A numerical method is said to be RN-stable if it preserves this contractivity property. After showing that, under slightly more stringent hypotheses on the Lipschitz constants and on the delay function , the solutions and are such that , in this paper we prove that RN-stable continuous Runge-Kutta methods preserve also this asymptotic stability property. Received March 29, 1996 / Revised version received August 12, 1996     

A delay-range-dependent uniformly asymptotic stability criterion for a class of nonlinear singular systems

This paper investigates a class of nonlinear singular systems. Based on the Lyapunov functional method and the free-weighting matrix method, a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Two examples are given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of nonlinear singular systems.     

On simple stability criteria for nonlinear neutral systems with multiple time delays

This work is concerned with the derivation of easily verifiable conditions for the asymptotic stability of a nonlinear nonautonomous neutral differential system. On introducing an adjusting function, the main results become less restrictive.     

Synchronization of nonlinear fractional order systems

This paper deals with the master-slave synchronization scheme for partially known nonlinear fractional order systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown state variables. For solving this problem we introduce a Fractional Algebraic Observability (FAO) property which is used as a main tool in the design of the master system. As numerical examples we consider a fractional order Rössler hyperchaotic system and a fractional order Lorenz chaotic system and by means of some simulations we show the effectiveness of the suggested approach.     

Controllability of nonlinear fractional dynamical systems

In this paper we establish a set of sufficient conditions for the controllability of nonlinear fractional dynamical systems. The results are obtained by using the recently derived formula for solution representation of systems of fractional differential equations and the application of the Schauder fixed point theorem. Examples are provided to illustrate the results.     

Finite-difference method for singular nonlinear systems

This paper presents a method for solving nonlinear system with singular Jacobian at the solution. The convergence rate in the case of singularity deteriorates and one way to accelerate convergence is to form bordered system. A local algorithm, with finite-difference approximations, for forming and solving such system is proposed in this paper. To overcome the need that initial approximation has to be very close to the solution, we also propose a method which is a combination of descent method with finite-differences and local algorithm. Some numerical results obtained on relevant examples are presented.     

Asymptotic stability for Bresse systems

In this paper consider a vibrating system of Bresse type in a one-dimensional bounded domain with a nonlinear damping acting in the equation of the shear angle displacement, and nonlinear localized damping in other equations. We show the asymptotic stability without imposing conditions about the equal-speed wave propagation, using a method developed by Lasiecka and Tataru [9].     

Asymptotic behavior results for nonlinear neutral delay difference equations

This paper is concerned with the nonlinear neutral delay difference equation

(∗)     

Controllability of fractional neutral stochastic functional differential systems

In this paper, we study a class of fractional neutral stochastic functional differential systems. We obtain the controllability of the stochastic functional differential systems by the Sadovskii’s fixed point theorem under some suitable assumptions. An example is given to illustrate the theory.