Some new simple stability criteria of linear neutral systems with a single delay

This article mainly considers the linear neutral delay-differential systems with a single delay. Using the characteristic equation of the system, new simple delay-independent asymptotic and exponential stability criteria are derived in terms of the matrix measure, the spectral norm and the spectral radius of the corresponding matrices. Numerical examples demonstrate that our criteria are less conservative than those of previous corresponding results [L.M. Li, Stability of linear neutral delay-differential systems, Bull. Aust. Math. Soc. 38 (1988) 339–344; G.D. Hu, G.D. Hu. Some simple criteria for stability of neutral delay-differential systems, Appl. Math. Comput. 80 (1996) 257–271; D.Q. Cao, Ping He, Sufficient conditions for stability of linear neutral systems with a single delay, Appl. Math. Lett. 17 (2004) 139–144; G.D. Hu, G.D. Hu, B. Cahlon, Algebraic criteria for stability of linear neutral systems with a single delay, J. Comput. Appl. Math. 135 (2001) 125–130].     

Simple criterion for asymptotic stability of interval neutral delay-differential systems

In this paper, the asymptotic stability of interval neutral delay-differential systems is investigated. A delay-independent criterion for the stability of the system is derived in terms of the spectral radius. Numerical computations are performed to illustrate the result.     

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.     

中立型时滞系统的稳定性改进判据

研究了含有时变时滞的不确定中立系统的时滞相关稳定性问题.假定不确定参数是范数有界的,通过构造新的Lyapunov泛函和使用更一般的时滞分解方法,得到了基于LMI新颖的时滞相关稳定条件,并且用Matlab LMI工具箱很容易地求解.数值实例表明本文方法所得结果优于现有文献中的结果.     

Novel stability criteria for neutral systems with multiple time delays

Based on the eigenvalues of characteristic equations, some new criteria are derived to ensure the asymptotic stability for a class of neutral differential equations with multiple time delays. Conditions obtained here are independent of the time delays and easy to be checked. When suitable f_j(·) (j = 1, 2, … , m) are chosen, the model studied in this paper will reduce to a simple form. Moreover, our results can resolve some nonlinear neutral problems which are seldom discussed. Finally, an example with numerical simulation is given to show the effectiveness of our method.     

Stability analysis of numerical methods for systems of neutral delay-differential equations

Stability analysis of some representative numerical methods for systems of neutral delay-differential equations (NDDEs) is considered. After the establishment of a sufficient condition of asymptotic stability for linear NDDEs, the stability regions of linear multistep, explicit Runge-Kutta and implicitA-stable Runge-Kutta methods are discussed when they are applied to asymptotically stable linear NDDEs. Some mentioning about the extension of the results for the multiple delay case is given.     

Algebraic criteria for stability of linear neutral systems with a single delay

The stability of linear neutral delay-differential systems with a single delay via Routh–Hurwitz and Schur–Cohn criteria is investigated. Some algebraic criteria for delay-independent stability are presented. These criteria may complement those reported in the literature. Finally, two examples illustrate the criteria.     

Some practical stability criteria for systems of linear differential equations

We examine some problems of practical stability of motion of linear systems when the initial state of the phase trajectory is contained in a ball in the l_p space. Various constraints on the phase state are considered. Parametric stability criteria and stability criteria under simultaneous constraints on the initial state and the perturbations are derived.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 62, pp. 99–104, 1987.     

A further note on stability criteria for uncertain neutral systems with mixed delays

This paper is a further note on stability criteria for uncertain neutral systems with mixed delays. We firstly employed a new method to estimate the upper bound of the derivative of functional, and novel stability criteria are presented for nominal neutral system, which will obtain less conservatism. Then, several sufficient stability conditions are proposed for neutral systems with polytopic uncertainty and linear fractional norm-bound uncertainty. Lastly, three numerical examples are given to demonstrate the effectiveness and merit of the proposed results. In Appendix, the stability criteria in Lu et al. [21] are rectified.     

Asymptotic stability criteria for linear systems of difference-differential equations of neutral type and their discrete analogues

Electrical networks containing lossless transmission lines are often modeled by difference-differential equations of neutral type. This paper finds sufficient conditions for asymptotic stability for linear systems of these equations. Also given is a modification of the direct method of Liapunov for difference equations. This method is applied to finding asymptotic stability criteria for the discrete analogs of the linear system of difference-differential equations.     

Global stability of synchronization between delay-differential systems with generalized diffusive coupling

Synchronization between general delay feedback systems coupled by generalized diffusive coupling with delay is studied. It is shown that the generalized diffusive coupling synchronizes the units much more effectively than the simple diffusive coupling. Sufficient conditions for the global stability of synchronization for systems of a quite general form are obtained.     

时滞依赖型中立系统的鲁棒稳定性分析

研究了一类不确定中立型系统的时滞依赖稳定性问题.利用基于LMI正定解的存在性,给出了一个新时滞依赖型稳定性判据,相比于已有文献本文具有低的保守性.最后通过数值算例验证了本文得到的结论的正确性和有效性.     

Stability criteria for uncertain neutral systems with interval time-varying delays

This paper investigates asymptotic stability problem for neutral system with interval time-varying delays and two classes of uncertainties. Delay-dependent and delay-independent criteria are proposed to guarantee the asymptotic stability for our considered systems. Lyapunov–Krasovskii functional and Leibniz–Newton formula are applied to find the delay-dependent stability results. Linear matrix inequality (LMI) approach is used to solve the proposed conditions. Finally, some numerical examples are illustrated to show the improvement of this paper.     

New stability criteria for a class of neutral systems with discrete and distributed time-delays: an LMI approach

In this paper, a problem of the asymptotic stability for a class of neutral systems with multiple discrete and distributed time-delays is considered. Lyapunov stability theory is applied to guarantee the stability for the systems. New discrete-delay-independent and discrete-delay-dependent stability conditions are derived in terms of the spectral radius and linear matrix inequality. By mathematical analysis, the stability criteria are proved to be less conservative than the ones reported in the current literatures. A numerical example is given to illustrate the availability of the proposed results.     

Asymptotic stability and instability criteria for nonautonomous systems

The classical criterion of asymptotic stability of the zero solution of equations x′ = f(t, x) is that there exists a function V (t, x), a(∥x∥) ≤ V (t, x) ≤ b(∥x∥) for some a, b ∈ K such that [(V)\dot] \dot{V} (t, x) ≤ −c(∥x∥) for some c ∈ K. In this paper, we prove that if V^{(m + 1)} \mathop {V}\limits^{(m + {1})} (t, x) is bounded on some set [tk − T, tk + T] × BH(tk → +∞ as k → ∞), then the condition that [(V)\dot] \dot{V} (t, x) ≤ −c(∥x∥) can be weakened and replaced by that [(V)\dot] \dot{V} (t, x) ≤ 0 and − (−[(V)\dot] \dot{V} (tk, x)| + − [(V)\ddot] \ddot{V} (tk, x)| + ⋯ + − V^(m) \mathop {V}\limits^{(m)} (tk, x)|) ≤ −c′(∥x∥) for some c′ ∈ K. Moreover, the author also presents a corresponding instability criterion. [1–10]