Stability Of Neutral Differential Equations Research Articles

New results on robust exponential stability of Takagi–Sugeno fuzzy for neutral differential systems with mixed time-varying delays

This study aims to analyse the robust exponential stability for neutral differential equations of the uncertain Takagi–Sugeno fuzzy system with distributed and discrete time interval delays by applying the Newton–Leibniz formula, the Lyapunov–Krasovskii functional, and the zero equations. By these methods, the less conservative exponential stability criteria are obtained for a special case of the generalized fuzzy of the neutral differential system. By applying Matlab LMI toolbox, the new conditions for exponential stability are obtained in the forms of linear matrix inequalities (LMIs), which can verify the numerical performance by the LMI toolbox of MATLAB. Finally, numerical examples are provided to manifest the efficiency and reduce the conservatism of the obtained results rather than the results which exist in the literature.

Partial Variable Stability for a Class of Nonlinear Systems with Time Delay

This article first gives a new class of integral inequalities. Then, as an application, the nonlinear neutral differential system with multiple delays is considered, and the trivial solution of the nonlinear neutral system with multiple delays is obtained. Uniform asymptotic Lipschitz stability. Obviously, the above system is a generalization of the traditional differential system. The purpose of this paper is to study the dual stability of neutral differential equations with delays, including equal asymptotically Lipschitz stability and uniformly asymptotic Lipschitz stability. The author uses the method of integral inequality to establish a double stability criterion. As a result, the local stability of differential equations is widely used in theory and practice, such as dynamic systems and control systems.

Generalization of integral inequalities and (c1, c1) stability of neutral differential equations with time-varying delays

Generalization of integral inequalities and (c₁, c₁) stability of neutral differential equations with time-varying delays

Study of Numerical Stability for Neutral Differential Equations with Delay by Θ- Method

Study of Numerical Stability for Neutral Differential Equations with Delay by Θ- Method

Some improved criteria on exponential stability of neutral differential equation

In this paper, some improved delay-dependent exponential stability criteria of the neutral delayed differential equation are expressed in terms of linear matrix inequalities (LMIs). Compared with some existing ones, our results are derived without the use of the mode transformation method and the bounding technique. Three numerical examples are provided to show the effectiveness of the proposed method and less conservatism of the obtained results.

New criteria for stability of neutral differential equations with variable delays by fixed points method

The linear neutral differential equation with variable delays is considered in this article. New criteria for asymptotic stability of the zero solution are established using the fixed point method and the differential inequality techniques. By employing an auxiliary function on the contraction condition, the results of this article extend and improve previously known results. The method used in this article can also be used for studying the decay rates of the solutions.

Fixed points and stability in neutral differential equations with variable delays

In this paper we consider a linear scalar neutral delay differential equation with variable delays and give some new conditions to ensure that the zero solution is asymptotically stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic stability theorem with a necessary and sufficient condition is proved. The results of Burton, Raffoul, and Zhang are improved and generalized.