Neutral Delay-differential Systems Research Articles

Equivalence and Reduction of Delay-Differential Systems

Equivalence and Reduction of Delay-Differential SystemsA new direct method is presented which reduces a given high-order representation of a control system with delays to a first-order form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann's strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural properties of the original system invariant.

Periodic solutions of a class of neutral differential models with feedback control

Sufficient conditions are obtained for the existence of positive periodic solutions of a class of neutral delay differential system with state-dependent delays and feedback control by using the theory of topological degree and some new analytical techniques. The analytical result obtained is not only of great interest in theory but also many applications such as biomathematics, which extends substantially the existing relevant existence results in the literature. As a demonstration, applying the obtained analysis results to a real complex neutral Lotka–Volterra population model, the existence criterion for positive periodic solutions is easily obtained. Especially, this method is more suitable to state-dependent delay.

An EP algorithm for stability analysis of interval neutral delay-differential systems

As well-known, evolutionary programming (EP) algorithms have been considered as promising techniques for global optimal search. The main objective of this paper is to develop a novel EP algorithm for the robust stability analysis of interval neutral delay-differential systems. Two main results are obtained in this paper. First a delay-dependent criterion is derived for ensuring the stability of degenerate neutral time-delay systems, and then by solving some optimization problems, which will be defined later, the robust stability of interval neutral delay-differential systems can be guaranteed. Two numerical examples are given to illustrate the results.

Delay-dependent stability analysis for uncertain neutral systems with time-varying delays

This paper investigates the stability of neutral delay-differential systems with mixed multiple time-varying delay arguments. Based on the Lyapunov functional method, and the relationship between the system states and the derivatives of these states, we present a new asymptotical stability criterion and a new robust stability criterion in terms of only one simple linear matrix inequality (LMI), which guarantees stability for such systems with time-varying delays. This LMI can be easily solved by various convex optimization algorithms. Two examples are given to illustrate the advantages of the proposed methods over the existing ones.

Global exponential stability analysis for neutral delay-differential systems: an LMI approach

For neutral differential systems with time-varying or constant delays, the problems of determining the global exponential stability and estimating the exponential convergence rate are investigated in this paper. By using the Lyapunov method, some useful criteria of global exponential stability for the systems are derived. These stability conditions are formulated as linear matrix inequalities (LMIs) which can easily be solved by various convex optimization algorithms. Numerical examples are given to illustrate the application of the proposed method.

Delay-dependent H-infinity filtering for neutral time-delay systems

This paper deals with the robust delay-dependent H-infinity filtering problem for neutral delay differential systems. The resulting filter is of the Luenberger observer type, and it guarantees that the filtering systems remains asymptotically stable and satisfies a prescribed H-infinity performance level. The Lyapunov stability theory and the descriptor model transformation are used for analysis of the system and are expected to be least conservative as compared with existing design methods. Some examples are provided to demonstrate the validity of proposed design approach.

A further note on stability criterion of linear neutral delay-differential systems

This paper is a further note which corrects an error of the paper by Park and Won. A new stability criteria which is less conservative than those in the literature is presented.

Some new simple stability criteria of linear neutral systems with a single delay

This article mainly considers the linear neutral delay-differential systems with a single delay. Using the characteristic equation of the system, new simple delay-independent asymptotic and exponential stability criteria are derived in terms of the matrix measure, the spectral norm and the spectral radius of the corresponding matrices. Numerical examples demonstrate that our criteria are less conservative than those of previous corresponding results [L.M. Li, Stability of linear neutral delay-differential systems, Bull. Aust. Math. Soc. 38 (1988) 339–344; G.D. Hu, G.D. Hu. Some simple criteria for stability of neutral delay-differential systems, Appl. Math. Comput. 80 (1996) 257–271; D.Q. Cao, Ping He, Sufficient conditions for stability of linear neutral systems with a single delay, Appl. Math. Lett. 17 (2004) 139–144; G.D. Hu, G.D. Hu, B. Cahlon, Algebraic criteria for stability of linear neutral systems with a single delay, J. Comput. Appl. Math. 135 (2001) 125–130].

Asymptotic Stability in a Neutral Delay Differential System with Variable Delays

By applying M-matrix theory and some new analysis techniques, we have succeeded in establishing the asymptotic stability of the zero solution of the pure-delay type neutral system with variable delays. The criteria obtained in this paper extend and improve the existing ones.

Design of robust [formula omitted] filter for a class of neutral systems: LMI optimization approach

In this paper, the design method of H ∞ filter for a class of neutral delay-differential systems is investigated. A linear matrix inequality (LMI) approach is proposed to design a robust H ∞ filter such that the filtering system remains asymptotically stable and the bound of H ∞ norm is minimized. The Lyapunov stability theory is used for analysis of the system. A numerical example illustrate the theoretical results.

Some sufficient conditions for exponential stability of linear neutral functional differential equations

Abstract In this paper, we give some sufficient conditions for exponential stability of linear neutral functional differential equations. The obtained results are extensions of the recent results in [D.Q. Cao, P. He, Stability criteria of linear neutral systems with a single delay, Appl. Math. Comput. 148 (2004) 135–143, D.Q. Cao, P. He, Sufficient conditions for stability of linear neutral systems with a single delay, Appl. Math. Lett. 17 (2004) 139–144], [G.-D. Hu, G.-D. Hu, X.F. Zou, Stability of linear neutral systems with multiple delays: boundary criteria, Appl. Math. Comput. 148 (2004) 707–715; J.H. Park, S. Won, A note on stability of neutral delay-differential systems, J. Franklin Inst. 336 (1999) 1–9] to linear neutral functional differential equations.

Simple algebraic criteria for stability of neutral delay-differential systems

The asymptotic stability of linear neutral systems with a single delay is investigated in this article. Based on the characteristic equation, new algebraic criteria for the stability of the system are derived in terms of the spectral radius of corresponding modulus matrices. The significance of our new criteria is that it takes into consideration the structure information of the system matrices, thus reducing the conservatism found in the literature. Numerical examples are given to demonstrate the new stability criteria and to compare them with the previous results in the literature.

Design of a dynamic output feedback controller for a class of neutral systems with discrete and distributed delays

The design problem for a dynamic output feedback controller for asymptotic stabilisation of a class of neutral delay differential systems with discrete and distributed time delays is investigated. A criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the Lyapunov method. A parameterised characterisation of the controllers is given in terms of the feasible solutions to the certain matrix inequalities, which can be solved by various convex optimisation algorithms. A numerical example is given to illustrate the availability of the proposed results.

On guaranteed cost control of neutral systems by retarded integral state feedback

In this paper, the guaranteed cost control problem for a class of neutral delay-differential systems with a given quadratic cost functions is investigated. The problem is to design a memory state feedback controller such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Some criteria for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the controllers is given in terms of the feasible solutions to the certain LMIs. A numerical example is given to illustrate the proposed method.

Robust Stability of Uncertain Neutral Delay Systems

The stability of a linear neutral delay-differential system is studied, where both the system matrices and time delays may be uncertain. A sufficient condition is derived to guarantee the perturbed system is robustly stable. The computation of acceptable upper bounds for system matrix uncertainties and time-delay perturbations is also discussed, and an example is finally illustrated.

Delay-dependent guaranteed cost stabilization criterion for neutral delay-differential systems: matrix inequality approach

In this paper, we address the problem of the guaranteed cost stabilization for a class of neutral delay-differential systems with a given quadratic cost function. Based on the Lyapunov method, delay-dependent criteria, which are expressed in terms of matrix inequalities, are proposed to guarantee the asymptotic stability of the system. The matrix inequalities can be easily solved by various efficient optimization algorithms.

Exponential stability assignment of neutral delay-differential systems by a class of linear–quadratic regulators

A method to construct a simple feedback law for neutral delay-differential systems is proposed. The feedback gain is determined with a solution of a matrix inequality, which can be solved numerically via the technique of solving finite-dimensional linear matrix inequalities. It is shown that the resulting closed-loop system is asymptotically stable, and if some transformation of variables is introduced, it is assured to have a pre-assigned degree of exponential stability. Moreover, it belongs to a class of linear–quadratic regulators. The design procedure is demonstrated and the effectiveness of the feedback is evaluated with a numerical simulation.

On robust stabilization for neutral delay-differential systems with parametric uncertainties and its application

This paper considers the problem of robust stabilization for uncertain neutral delay-differential systems. Based on the Lyapunov method, a delay-dependent criterion for determining the stability of systems is obtained in terms of matrix inequalities, which can be easily solved by efficient convex optimization algorithms. Then, the method presented is extended to systems with controller gain variations, that is, the design problem for the nonfragile controller is considered. A numerical example is included to illustrate the design procedure of the proposed method.

Insensitivity of a class of LQ regulators of neutral systems

It is well known that the linear quadratic regulators of finite dimensional linear systems have the insensitivity property. In this paper, as a particular class of infinite dimensional systems, a neutral delay-differential system is considered as a plant. A class of linear quadratic regulators is constructed for the plant using a simple feedback law, which does not require real-time either integral or derivative operations. The feedback gain is calculated by solving a finite dimensional linear matrix inequality. First, it is shown that the regulator satisfies the circle condition. Then, its sensitivity against the parameter variations is evaluated. In the single-input case, it is done by calculating the absolute value of the sensitivity function. In the multi-input case, it is done by the so-called “comparison sensitivity” method where the sensitivities of the closed-loop system and the open-loop system are compared based on certain sensitivity indices. Procedures used for the investigation of the regulator's properties are based on natural extension of methods proposed by Perkins and Cruz for the finite dimensional case. As a result, it is found that the class of linear quadratic regulators of neutral systems, similarly to finite dimensional systems, has the insensitivity property. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(2): 28–34, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20013

不確かな中立型むだ時間系のコスト保証制御

An alternative method is proposed to construct a guaranteed cost control law for neutral delay-differential systems with uncertain parameters. The feature of this method is that it is fit for the state space not W12 but M2, in the points : i) the form of the feedback law, ii) the form of the cost functional, and iii) the form of Liapunov function. A sufficient condition to obtain the feedback law is given, and its necessary and sufficient condition is introduced with linear matrix inequalities (LMIs). The feedback gain can be calculated with a solution of the LMIs. Furthermore, the upper bound of the cost functional can be minimized by a convex optimization. A numerical example is given to demonstrate the design procedure.