Delay-differential Systems Of Neutral Type Research Articles

A Stability Criterion for the System of High-Order Neutral Delay Differential Equations

We study the delay–dependent stability of linear high-order delay differential systems of neutral type. We firstly derive a bound of the unstable eigenvalues of the neutral systems. The bound of the unstable eigenvalues involves only the norms of the matrices of lower size. Then, using the argument principle, we present some stability criterion that is a necessary and sufficient condition for the delay–dependent stability of the neutral systems. Furthermore, we provide an efficient numerical algorithm for checking the stability of the neutral systems. Some numerical examples are given to illustrate the main results which extend those in the literature.

On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays

In this paper, we propose a new stability criterion for uncertain neutral systems. The considered system has time-varying structured uncertainties and time-varying delay. Based on the Lyapunov method, a delay-dependent criterion for asymptotic stability is derived in terms of LMI (linear matrix inequality). Numerical examples are given to show the effectiveness of our results.

On Computing the Maximum Time-Delay Bound for Stability of Linear Neutral Systems

This note is concerned with the stability problem of linear delay-differential systems of neutral type. A discretized Lyapunov functional approach is developed. The resulting stability criterion is formulated in the form of a linear matrix inequality. For nominal systems, the analytical results can be approached with fine discretization. Numerical examples show significant improvement over approaches in the literature.

On new stability criterion for delay-differential systems of neutral type

In this paper, a novel stability criterion is presented for neutral differential systems. Based on the Lyapunov method, the stability criterion is derived in terms of linear matrix inequalities which can be easily solved by efficient convex optimization algorithms. Numerical examples are included to show the effectiveness of the proposed method.

On the design of observer-based controller of linear neutral delay-differential systems

In this note, the observer-based control problem for a class of linear delay-differential systems of neutral type is investigated. Using the Lyapunov method, a criterion for asymptotic stability is derived in terms of matrix inequalities, which solved by convex optimization algorithms. A numerical example is given to illustrate the proposed method.

A DISCRETIZED LYAPUNOV FUNCTIONAL APPROACH TO STABILITY OF LINEAR DELAY-DIFFERENTIAL SYSTEMS OF NEUTRAL TYPE

This paper considers the stability problem of linear delay-differential systems of neutral type. A discretized Lyapunov functional approach is developed. The resulting stability criteria are formulated in the form of a linear matrix inequality. For nominal systems, the analytical results can be approached with fine discretization. For uncertain systems, the new approach is much less conservative. Numerical examples show significant improvement over approaches in the literature.

Robust stability of uncertain delay-differential systems of neutral type

This paper focuses on the stability problem for neutral delay-differential systems with norm-bounded, and possibly time-varying, uncertainty. The time-delay is assumed constant and known. A stability criterion that is formulated in a linear matrix inequality (LMI) form is derived. Numerical examples show that the results obtained by this new criterion significantly improve the estimate of stability limit over some existing results in the literature.

Evaluation of quadratic cost functionals for neutral systems: the frequency-domain approach

Abstract As shown in Grabowski (1983), the problem of evaluation of the quadratic performance index for delay-differential systems of neutral type can be effectively solved by the use of Lyapunov functionals. In this paper another solution to that problem, based on the frequency-domain approach, is proposed. With the use of Plancherel's theorem and other tools of complex analysis, this task is reduced to a Riemann-Hilbert problem, an explicit solution to which is found by elementary methods. Our results can be regarded as a generalization of those due to Walton and Marshall (1984, 1987). Two simple examples of application are also provided.

Evaluation of quadratic cost functionals for neutral systems: the frequency-domain approach

Abstract As shown in Grabowski (1983), the problem of evaluation of the quadratic performance index for delay-differential systems of neutral type can be effectively solved by the use of Lyapunov functionals. In this paper another solution to that problem, based on the frequency-domain approach, is proposed. With the use of Plancherel's theorem and other tools of complex analysis, this task is reduced to a Riemann-Hilbert problem, an explicit solution to which is found by elementary methods. Our results can be regarded as a generalization of those due to Walton and Marshall (1984, 1987). Two simple examples of application are also provided.

On the Pointwise Completeness of Delay-Differential Systems of Neutral Type

Necessary and sufficient conditions for pointwise completeness of delay-differential systems of neutral type are given. It is shown that there exist second order delay-differential systems of neutral type which are not pointwise complete. It is also proved that degeneracy in case of nth order delay-differential systems of neutral type with one delay can start no later than $(n - 1)h$, where h is the delay.