Stability Criteria For Neutral Systems Research Articles

New Delay-Partitioning LK-Functional for Stability Analysis with Neutral Type Systems

This paper investigates the stability issues associated with neutral-type delay systems. Firstly, the delay-partitioning method is employed to construct a brand-new LK-functional candidate. The discrete delay and a neutral delay are divided into several piecewise points through a relaxable sequence of constant numbers, are increasing at a steady rate and are not larger than 1. Secondly, to fully use the interconnection information among the delayed state vectors, a new LK-functional is constructed. Thirdly, the recently published single/multiple integral inequalities are employed to bound the derivative of the newly developed LK function. Finally, a novel stability criterion for neutral systems is developed based on the above treatment. Furthermore, a new corollary is also proposed for the condition of τ=h. The benefits and productivities of our method are demonstrated by numerical examples.

带有混合时滞和非线性扰动的中立系统指数稳定性改进的判别准则

带有混合时滞和非线性扰动的中立系统指数稳定性改进的判别准则

Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances

It is well-known that the stability analysis of time-delay systems is a key step to design appropriate controllers and/or filters for those systems. In this paper, the problem of the delay-dependent stability analysis of neutral systems with mixed interval time-varying delays with/without nonlinear perturbations is revisited. Bounded derivatives of the discrete and neutral delays with upper-bounds not limited to be strictly less than one are considered. New stability criteria are developed using the Lyapunov Krasovskii methodology which are expressed in terms of linear matrix inequalities (LMIs). An augmented Lyapunov Krasovskii functional (LKF) utilizing triple integral terms and the descriptor transformation is employed to this aim. In addition, advanced techniques such as Wirtinger-based single and double-integral inequalities, delay decomposition technique combined with the reciprocally convex approach, as well as a few effective free-weighting matrices are employed to achieve less conservative stability conditions. Comprehensive benchmarking numerical examples and simulation studies demonstrate the effectiveness of the proposed stability criteria with respect to some recently published results. The efficacy of the modern integral inequalities are also emphasized against the conventional Jensen׳s inequalities.

Improved mixed‐delay‐dependent asymptotic stability criteria for neutral systems

This study concerns the problem of asymptotic stability analysis for neutral systems with mixed delays. Some simple and less conservative criteria are firstly proposed based on the Wirtinger-based integral inequality. Then, incorporating the delay-decomposition idea with the augmented Lyapunov–Krasovskii functional, a new augmented delay-decomposition Lyapunov–Krasovskii functional is constructed. In addition, the Wirtinger-based integral inequality is sufficiently utilised to cope with the derivative of the constructed functional. Those treatments lead to less conservatism, and an improved asymptotic stability condition is obtained. Finally, a numerical example is given to show the effectiveness and benefit of the proposed criteria.

New Delay-dependent stability criteria for neutral systems with time-varying delay using delay-decomposition approach

This paper concerns with the problem of asymptotic stability for neutral systems with timevarying delays. With the introduction of delay-decomposition approach, some new delay-dependent stability criteria are established and formulated in the form of linear matrix inequalities. Both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

New exponential stability criteria for neutral system with time-varying delay and nonlinear perturbations

In this paper, the problem of exponential stability for neutral system with time-varying delay and nonlinear perturbations is investigated. By using the technology of model transformations, based on a linear matrix inequality (LMI) and a generalized Lyapunov-Krasovskii function, a new criterion for exponential stability with delay dependence is obtained. Due to a new integral inequality, the result is less conservative. Finally, some numerical examples are presented to illustrate the effectiveness of the method.

Exponential Stability Criteria for Neutral System with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper focuses on the issue of robustly exponential stability for uncertain neutral systems with mixed time-varying delays and nonlinear perturbations. Some new sufficient conditions dependent on the delays are derived in terms of Lyapunov-Krasovskii functionals combined with free-weighting matrices. Two numerical examples are given to show the effectiveness of the proposed method.

Delay-dependent exponential stability criteria for neutral systems with interval time-varying delays and nonlinear perturbations

This paper investigates the problem of global exponential stability for neutral systems with interval time varying delays and nonlinear perturbations. It is assumed that the state delay belongs to a given interval, which means that both the lower and upper bounds of the time-varying delay are available. The uncertainties under consideration are norm-bounded. Based on the Lyapunov–Krasovskii stability theory, delay-partitioning technique and lower bounds lemma, less conservative delay-dependent exponential stability criteria are derived in terms of linear matrix inequalities (LMIs) with fewer decision variables than the existing ones. Numerical examples are given to show the effectiveness of the proposed method.

Novel delay-dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations

This paper investigated the problem of delay-dependent robust stability criteria for neutral systems with mixed time-varying delays and nonlinear perturbations. A piecewise delay method is used in this paper, the variation interval of the time delay is divided into two subintervals by introducing its central point. Then, by employing the new Lyapunov–Krasovskii functional and linear matrix inequality technique, some new sufficient conditions are obtained. At last, numerical examples are provided to demonstrate the effectiveness of the obtained results.

A delay decomposition approach to stability analysis of neutral systems with time-varying delay

This paper presents novel stability criteria for neutral systems with time-varying delay. By developing a delayed decomposition approach, information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs). Then, based on the Lyapunov method, delay-dependent stability criteria are devised by taking the relationship between terms in the Leibniz-Newton formula into account. Criteria are derived in terms of LMIs, which can be easily solved by using various convex optimization algorithms. Three illustrative numerical examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.

On delay-dependent robust stability of uncertain neutral systems with interval time-varying delays

In this paper, the problem of a new delay-dependent robust stability criterion for neutral systems is investigated. The considered system has time-varying structured uncertainties and interval time-varying delays. Based on the Lyapunov method, a delay-dependent criterion for asymptotic stability is established in terms of LMI (linear matrix inequality). Numerical examples are carried out to support the effectiveness of our results.

Stability criteria for neutral systems with time‐varying delays and nonlinear uncertainties

The asymptotic stability problem for a class of neutral systems with time‐varying delays and nonlinear uncertainties is investigated in this paper. LMI‐based delay‐dependent criteria are proposed to guarantee the asymptotic stability of the considered systems. New Lyapunov‐Krasovskii functional and Leibniz‐Newton formulae are used to find the delay‐dependent stability results. Finally, some numerical examples are illustrated to show the improved results from using this method.

Novel stability criteria for neutral systems with multiple time delays

Abstract 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.

Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems

In this paper, an augmented Lyapunov functional is proposed to investigate the asymptotic stability of neutral systems. Two methods with or without decoupling the Lyapunov matrices and system matrices are developed and shown to be equivalent to each other. The resulting delay-dependent stability criteria are less conservative than the existing ones owing to the augmented Lyapunov functional and the introduction of free-weighting matrices. The delay-independent criteria are obtained as an easy corollary. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods. Copyright © 2005 John Wiley & Sons, Ltd.

A Delay-Dependent Stability Criterion of Neutral Systems and its Application to a Partial Element Equivalent Circuit Model

The real circuit model, such as a partial element equivalent circuit (PEEC), can be represented as a delay differential equation (DDE) of neutral type. The study of asymptotic stability of this kind of systems is of much importance due to the fragility of DDE solvers. Based on a descriptor system approach, new delay-dependent stability results are derived by introducing some free weighting matrices. As an application of the results, the delay-dependent stability problem of a PEEC model is investigated. The comparison of the results with the existing ones is finally given by using the PEEC model and another numerical example.

Stability of linear descriptor systems with delay: a Lyapunov-based approach

The Lyapunov second method is developed for linear coupled systems of delay differential and functional equations. By conventional approaches such equations may be reduced to the neutral systems and the known results for the latter may be exploited. In the present paper we introduce a new approach by constructing a Lyapunov–Krasovskii functional that corresponds directly to the descriptor form of the system. Moreover, by representing a neutral system in the descriptor form we obtain new stability criteria for neutral systems which are less conservative than the existing results. Sufficient conditions for delay-dependent/delay-independent stability and for robustness of stability with respect to small delays are given in terms of linear matrix inequalities. Illustrative examples show the effectiveness of the method.