Stability Analysis Of Neutral Systems Research Articles

A Novel Lyapunov functional with application to stability analysis of neutral systems with nonlinear disturbances

It is well-known that the global asymptotic stability analysis of neutral systems is an important concept in designing the appropriate controllers or filters for this class of systems. This paper carries out a delay-independent stability analysis of neutral systems possessing discrete time delays in the states and discrete neutral delays in the time derivative of the states in the presence of nonlinear disturbances. Some new global asymptotic stability criteria are proposed by introducing a novel Lyapunov functional. The obtained delay-independent stability criteria establish some simple and easily verifiable mathematical expressions involving the elements of the system matrices and the disturbance parameters of the neutral system. Different from the most of the previously reported stability results for neutral systems, the conditions obtained in this paper are not expressed in terms the Linear Matrix Inequalities (LMIs). Therefore, the criteria presented in this paper can be considered as the alternative results to previously published stability results stated in the LMI forms. A comparison between the results of this paper and some of previously published corresponding stability results is made to substantiate the significant improvement of the proposed results. A constructive numerical example is also presented to show applicability and the effectiveness of the proposed stability condition.

Stability analysis of neutral systems with mixed interval time-varying delays and nonlinear disturbances

This paper studies the problem of stability analysis for neutral systems with mixed time-varying delays and nonlinear disturbances. Improved stability criteria are obtained by applying augmented Lyapunov-Krasovskii methodology. First, a novel Lyapunov–Krasovskii functional containing the intersection relationship terms about mixed time-varying delays and their upper-lower bounds with lower bounds limited to be strictly greater than zero is fully established. Second, the upper bounds for integral terms presented are accurately estimated based on integral intervals decomposition approach. Third, a less conservative stability condition in terms of linear matrix inequality is derived by utilizing a new quadratic inequality technology. In the end, two numerical examples are given to illustrate the effectiveness and the advantages of the proposed method.

Stability analysis of uncertain neutral systems with discrete and distributed delays via the delay partition approach

This paper focuses on the stability analysis for neutral systems with discrete and distributed constant time-delays. Lyapunov-Krasovskii functionals (LKFs) are constructed by non uniformly dividing the whole delay interval into multiple segments and choosing proper functionals with different weighting matrices coressponding to different segments in the LKFs. By employing these LKFs, some new delay-derivative-dependent stability criteria are established for the neutral system in the delay partition approach. By utilizing the delay partition approach, the obtained stability criteria are stated in terms of linear matrix inequalities. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed approach less conservative than the existing ones.

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.

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.

Delay dependent stability analysis of neutral systems with mixed time-varying delays and nonlinear perturbations

This paper is concerned with the problem of stability of neutral systems with interval time-varying delays and nonlinear perturbations. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties. A new delay-dependent stability condition is derived in terms of linear matrix inequality by constructing a new Lyapunov functional and using some integral inequalities without introducing any free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters

This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequality (LMI) by constructing new Lyapunov–Krasovskii functionals via generalized eigenvalue problems (GEVPs). The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Delay-Dependent Stability Analysis of Neutral Systems Using Positive Polynomials Optimization

The main goal of this paper is to investigate the stability of neutral systems, by using some features of the method introduced by Zhang et al. (2003) for the standard time-delay case. The central idea consists in replacing the delay by some appropriate Pade approximation, obtaining a (sufficient) delay-dependent stability condition for the neutral system. Such a condition can be rewritten as a positivity constraint on a two-variable matrix polynomial, leading to an effective computation of the delay margin by using sum-of-squares representations of multivariable positive matrix polynomials.

Stability analysis of neutral systems with mixed delays

The stability of neutral systems with mixed delays is studied in this paper. A new discretized Lyapunov functional method is proposed. The method in this paper is less conservative than the existing ones and the results are very close to the analytical results. In addition, this method allows the coefficient matrix of the neutral term to have time-varying uncertainties.

On robust stability of linear neutral systems with time-varying delays

The application of the direct Lyapunov method to the stability analysis of neutral systems with time-varying delays usually encounters a restrictive assumption on the function in the right side of the differential equation. This function is supposed to satisfy the Lipschitz condition with respect to the delayed state derivative with a constant less than 1. In the present paper, we extend the input–output approach to consider the stability of neutral type systems with uncertain time-varying delays and norm-bounded uncertainties. The assumption on the Lipschitzian constant can then be avoided. Sufficient stability criteria are derived in the frequency domain and the time domain, where the descriptor discretized Lyapunov–Krasovskii functional is applied. As a by-product, new necessary conditions for neutral-delay-independent/retarded-delay-dependent stability criteria are obtained. The method can be easily extended to L2-gain analysis and can be applied to design problems.

Stability analysis of neutral systems with distributed delays

The stability of neutral systems with distributed delays is investigated in this paper. A modified Lyapunov–Krasovskii functional is constructed to study this class of systems. The proposed stability criterion is discrete-, distributed- and neutral-delay-dependent. In addition, by this method one can study the case when the coefficient matrix of the neutral delay term is time-varying uncertain. The reduced conservatism is illustrated in a numerical example.

A Delay-Partitioning Projection Approach to Stability Analysis of Neutral Systems

This paper introduces a new effective approach to study the stability of neutral systems. By employing a special Lyapunov-Krasovskii functional form based on delay partitioning, delay-dependent stability criteria are established for the nominal and the uncertain case (polytopic type) in terms of linear matrix inequalities (LMI). Numerical examples are employed to illustrate that the delay-partitioning projection approach can be applied to estimate the upper bounds for the delays for the system to maintain stability. Judging from these numerical results, the stability criteria obtained are less conservative than those of existing methods.

Stability analysis of neutral systems: a delay-dependent criterion

The main goal of this paper is to investigate the stability of neutral systems, by using the comparison method introduced by Zhang, Knospe and Tsiotras [13] for the standard time-delay case. The central idea consists in replacing the delay by two appropriate Pade approximations, obtaining two comparison systems whose robust stability give a simple delay-dependent stability condition for the (nominal) neutral system. Such a condition guarantees, as in the standard time-delay case, an a priori upper bound for the degree of conservatism induced by the comparison method. This degree depends on the order of the Pade approximation and its estimation makes the difference between this method and other approaches encountered in the literature. The effective computation of the delay margin is reduced to a set of finite dimensional LMI’s .

Stability analysis for neutral systems with mixed delays

Relationships between system states contained in the neutral equation are used to address the delay-dependent stability of a neutral system with time-varying state delay. Using linear matrix inequalities, we present a new asymptotic stability criterion, and a new robust stability criterion, for neutral systems with mixed delays. Since the criteria take into account the sizes of the neutral delay, discrete delay and the derivative of discrete delay, they are less conservative than those produced by previous approaches. Numerical examples are presented to demonstrate that these criteria are indeed more effective.

A new delay-dependent criterion for neutral systems with multiple delays

In this paper, the problem of the stability analysis for neutral systems with multiple delays is investigated. Using Lyapunov method, we present, a new delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs), which can be easily solved by various convex optimization algorithms. A numerical example is given to illustrate the effectiveness of the proposed method.

A note on the stability analysis of neutral systems with multiple time-delays

The asymptotic stability of linear neutral systems with multiple delays is investigated. A delay-independent criterion for the stability of the system is derived in terms of the spectral radius. A numerical example shows the effectiveness of the proposed method.