Systems Of Neutral Type Research Articles

Necessary and Sufficient Conditions for BIBO-Stability of Some Fractional Delay Systems of Neutral Type

In this note, bounded-input bounded-output (BIBO)-stability of a large class of neutral type fractional delay systems is investigated. Necessary and sufficient conditions of BIBO-stability are presented for the intended class of systems (the sufficient conditions have been provided for a more general case in the previous studies). Two lemmas are provided for checking a prerequisite imposed on the considered class of systems. Finally, two numerical examples are given to illustrate the obtained results.

On Asymptotic Behaviour of Solutions to n‐Dimensional Systems of Neutral Differential Equations

This paper presents the properties and behaviour of solutions to a class of n‐dimensional functional differential systems of neutral type. Sufficient conditions for solutions to be either oscillatory, or limt→∞yi(t) = 0, or limt→∞|yi(t)| = ∞, i = 1,2, …, n, are established. One example is given.

ROBUST TRACKING AND DISTURBANCE REJECTION FOR DECENTRALIZED NEUTRAL TIME-DELAY SYSTEMS

AbstractThe decentralized robust servomechanism problem, which is to design decentralized stabilizing controllers such that each decentralized output robustly tracks a given reference signal in the presence of certain disturbances, is considered for linear time-invariant time-delay systems of neutral type with discrete delays. The reference signals and the disturbance are assumed to satisfy a linear constant-coefficient delay-differential equation of neutral type with discrete delays. Necessary and sufficient conditions for the solvability of this problem are derived. The structure of the controller which solves this problem is also presented.

A new result on stability analysis for stochastic neutral systems

This paper discusses the mean-square exponential stability of stochastic linear systems of neutral type. Applying the Lyapunov–Krasovskii theory, a linear matrix inequality-based delay-dependent stability condition is presented. The use of model transformations, cross-term bounding techniques or additional matrix variables is all avoided, thus the method leads to a simple criterion and shows less conservatism. The new result is derived based on the generalized Finsler lemma (GFL). GFL reduces to the standard Finsler lemma in the absence of stochastic perturbations, and it can be used in the analysis and synthesis of stochastic delay systems. Moreover, GFL is also employed to obtain stability criteria for a class of stochastic neutral systems which have different discrete and neutral delays. Numerical examples including a comparison with some recent results in the literature are provided to show the effectiveness of the new results.

A new model transformation method and its application to extending a class of stability criteria of neutral type systems

This paper proposes a generalized equivalent model transformation method, which can include methods proposed by Fridman et al. and Bellen et al., for the stability analysis of a class of neutral type systems. By using the proposed model transformation method, a class of existing stability criteria derived by the Lyapunov functional approach can be extended to less conservative ones in terms of nonlinear matrix inequalities. Furthermore, procedures to solve these nonlinear matrix inequalities are also proposed. Illustrative examples are presented to demonstrate the effectiveness of the proposed model transformation method.

Absolute Interval Stability of Indirect Regulating Systems of Neutral Type

The Lyapunov direct method with the Lyapunov−Krasovskiy functional is under investigation. We proved sufficient criteria of stability, namely, absolute by nonlinearity and interval by parameters. Criteria of stability and estimates of convergence of solutions are given in the form of constructive algebraic inequalities.

Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients

This paper investigates the exponential-type stability of linear neutral delay differential systems with constant coefficients using Lyapunov-Krasovskii type functionals, more general than those reported in the literature. Delay-dependent conditions sufficient for the stability are formulated in terms of positivity of auxiliary matrices. The approach developed is used to characterize the decay of solutions (by inequalities for the norm of an arbitrary solution and its derivative) in the case of stability, as well as in a general case. Illustrative examples are shown and comparisons with known results are given.

Computation of critical parameters for neutral type time delay systems

Abstract In this paper, a procedure for the computation of the Lyapunov matrix of neutral type systems, with delays multiple of a basic one, is recalled: It consists in solving a boundary value problem for a delay free system of matrix equations. The important property that the elements of the spectrum of the delay system that are symmetric with respect to the imaginary axis belong to the spectrum of the delay free system is also established. This property is exploited for the determination of the critical values of the time delay system.

The Exact Controllability Property of Neutral Type Systems by the Moment Problem Approach Revisited

In a recent paper authors gave an analysis of the exact controllability problem via the moment problem approach. Namely, the steering conditions of controllable states are formulated as a vectorial moment problem using some Riesz basis. One of the main difficulties was the choice of the basis as, in general, a basis of eigenvectors does not exist. In this contribution we use a change of control by a feedback law and modify the structure of the system in such a way that there exists a basis of eigenvectors which allows a simpler expression of the moment problem. Hence, one obtains the result on exact controllability and on the time of exact controllability.

Robust stability of neutral systems: A discretized Lyapunov functional method

This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method.

NOVEL ROBUST DELAY-DEPENDENT CRITERION FOR ABSOLUTE STABILITY OF LUR'E SYSTEMS OF NEUTRAL TYPE

This letter considers uncertain Lur'e systems of neutral type with sector and slope restrictions. By constructing a new Lyapunov functional, a novel delay-dependent criterion for absolute stability is derived in terms of linear matrix inequalities (LMIs). Two numerical examples are illustrated to show the effectiveness of the proposed method.

Asymptotic properties of solutions to n-dimensional neutral differential systems

In this paper, we study the behaviour of solutions to functional differential systems of neutral type. We find sufficient conditions for solutions either to be oscillatory or to decay to zero. One example is included.

New results for global stability of a class of neutral-type neural systems with time delays

This paper studies the global convergence properties of a class of neutral-type neural networks with discrete time delays. This class of neutral systems includes Cohen–Grossberg neural networks, Hopfield neural networks and cellular neural networks. Based on the Lyapunov stability theorems, some delay independent sufficient conditions for the global asymptotic stability of the equilibrium point for this class of neutral-type systems are derived. It is shown that the results presented in this paper for neutral-type delayed neural networks are the generalization of a recently reported stability result. A numerical example is also given to demonstrate the applicability of our proposed stability criteria.

Modal control of multi-input systems of neutral type with retarded argument

We suggest a special choice of a basis in the linear span of columns of the “controllability matrix” for multi-input systems of neutral type with retarded argument, which permits one to obtain an effective sufficient solvability condition for the modal control problem for such systems. The proof of this condition provides a constructive way for designing the desired regulator by the feedback principle on the basis of the solution of linear algebraic systems over the ring of bivariate polynomials.

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.

On strong regular stabilizability for linear neutral type systems

The problem of strong stabilizability of linear systems of neutral type is investigated. We are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts. This is the case when the main part of the neutral equation is not assumed to be stable in the classical sense. We discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls. The method covers the case of multivariable control and is essentially based on the idea of infinite-dimensional pole assignment proposed in [G.M. Sklyar, A.V. Rezounenko, A theorem on the strong asymptotic stability and determination of stabilizing controls, C. R. Acad. Sci. Paris Ser. I Math. 333 (8) (2001) 807–812]. Our approach is based on the recent results on the Riesz basis of invariant finite-dimensional subspaces and strong stability for neutral type systems presented in [R. Rabah, G.M. Sklyar, A.V. Rezounenko, Stability analysis of neutral type systems in Hilbert space, J. Differential Equations 214 (2) (2005) 391–428].

Extensively augmented Lyapunov functional approach for the stability of neutral time-delay systems

The problem of stability for linear time-delay systems of neutral type is taken into consideration. A new extensively augmented Lyapunov-Krasovskii functional is introduced and a sufficient delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Utilisation of any model transformation method or any kind of bounding for the cross terms are avoided in the stability analysis. Moreover, in order to reduce the complexity of the solution of the LMI set, the proposed method does not also employ any free weighting matrix relaxation approach. Two numerical examples are illustrated to indicate the effectiveness of the proposed method.

Multiquadric approximation scheme on the numerical solution of delay differential systems of neutral type

In this paper, the aim is to present the multiquadric approximation scheme on the numerical solution of delay differential systems of neutral type. In presenting the process of the solution, the error estimation and run time of the method is introduced. We present the advantages of using the method and compare it with other methods. Comparing the numerical results obtained from the other methods, demonstrate the high accuracy and the efficiency of the proposed method. Also, we present some experiments in which numerical results show that the method works excellently, even where the data points are scattered. This indicates that the method is stable too.

Delay-independent robust guaranteed-cost control for uncertain linear neutral systems

This article concerns the delay-independent guaranteed-cost control problem via memoryless state feedback for a class of neutral-type systems with structural uncertainty and a given quadratic cost function. New delay-independent conditions for the existence of the guaranteed-cost controller are presented in the term of LMIs. An algorithm involving optimization is proposed to design a controller achieving an optimal guaranteed-cost, such that, the system can be stabilized for all admissible uncertainties. A numerical example is provided to illustrate the feasibility of the proposed method.

Stabilizing controller design for delay systems of neutral type

Stabilizing controller design for delay systems of neutral type