Differential Systems Of Neutral Type Research Articles

Modal controllability for systems of neutral type in classes of differential-difference controllers

We propose a solution for the modal controllability problem for linear autonomous differential systems of neutral type with commensurate delays in two classes of differentialdifference controllers.

Delay-dependent stability of numerical methods for delay differential systems of neutral type

We are concerned with stability of numerical methods for delay differential systems of neutral type. In particular, delay-dependent stability of numerical methods is investigated. By means of the H-matrix norm, a necessary and sufficient condition for the asymptotic stability of analytic solution of linear neutral differential systems is derived. Then, based on the argument principle, sufficient conditions for delay-dependent stability of Runge–Kutta and linear multi-step methods are presented, respectively. Furthermore, two algorithms are provided for checking delay-dependent stability of analytical and numerical solutions, respectively. Numerical examples are given to illustrate the main results.

Oscillation theorems for impulsive parabolic differential system of neutral type

In this paper, oscillatory properties of solutions to a nonlinear impulsive parabolic differential system of neutral type are investigated. A series of sufficient conditions are established for problems with Robin and Dirichlet boundary conditions. Examples are provided to confirm the validity of the analysis.

Finite spectrum assignment problem for a differential system of neutral type

For a linear autonomous system of neutral type with commensurable delays, we obtain solvability conditions for the finite spectrum assignment problem and construct a dynamic state feedback in the state providing an arbitrary finite spectrum of the closed-loop system. By choosing the assigned spectrum, one can make the closed-loop system asymptotically stable. The results are illustrated by examples.

Asymptotic Growth of Solutions of Neutral Type Systems

We consider a differential system of neutral type with distributed delay. We obtain a precise norm estimation of semigroup generated by the operator corresponding to the system in question. Our result is based on a spectral analysis of the operator and some uniform estimation of norms of the exponentials of matrices. We also discuss the stability properties of corresponding solutions and the existence of the fastest growing solution.

Non-oscillatory Solutions of Odd Order Linear Functional Differential System of Neutral Type with Distributed Delay

In the present paper we establish explicit and easy computable sufficient conditions for existing of several types of non-oscillatory solutions of linear delayed system of neutral type with distributed delay. The results are proved by numerical range technique, and generally they are applicable in the case of non-monotone measures too.

Non-Oscillatory Solutions of Linear Delay Functional Differential System of Neutral Type

In this paper, we consider the non-oscillatory solutions of linear delay functional differential system of neutral type, from which we obtain some new sufficient conditions of non-oscillation.

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.

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.

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.

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.

Stability analysis and H ∞ filtering for delay differential systems of neutral type

Stability analysis and H∞ filter design for linear neutral systems is discussed. First, a new Lyapunov–Krasovskii functional is constructed to derive a new less conservative delay-dependent stability condition. It is then shown that the introduction of more free matrices sometimes cannot help reduce the conservatism of the obtained conditions. This new criterion is applied to designing a suitable H∞ filter of the Luenberger observer type, and a new design scheme is formulated in terms of the feasibility of a linear matrix inequality. Finally, some examples are given to illustrate the effectiveness of the proposed approach.

Convex Optimization Approach to Dynamic Output Feedback Control for Delay Differential Systems of Neutral Type

In this paper, the design problem of the dynamic output feedback controller for the asymptotic stabilization of a class of linear delay differential systems of the neutral type is considered. A criterion for the existence of such controller is derived based on the matrix inequality approach combined with the Lyapunov method. A parametrized characterization of the controller is given in terms of the feasible solutions to certain matrix inequalities, which can be solved by various convex optimization algorithms. A numerical example is given to illustrate the proposed design method.

Oscillation of differential systems of neutral type

We study oscillatory properties of solutions of systems $$\left[ {y_1 \left( t \right) - a\left( t \right)y_1 \left( {g\left( t \right)} \right)} \right]^\prime = p_1 \left( t \right)y_2 \left( t \right),$$ $$y'_2 \left( t \right) = - p_2 \left( t \right)f\left( {y_1 \left( {h\left( t \right)} \right)} \right),\quad t \geqslant t_0 .$$ .

Robust guaranteed cost control for uncertain linear differential systems of neutral type

In this paper, the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated. The uncertainty is assumed to be norm-bounded and time-varying nonlinear. The problem is to design a state feedback control laws such that the closed-loop system is robustly stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay. A criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the Lyapunov method. A parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities. A numerical example is given to illustrate the proposed method.

Oscillatory behaviour in functional differential systems of neutral type

In this paper are obtained several criteria for oscillations of a class of autonomous functional differential systems of neutral type.

Oscillatory properties of solutions of three-dimensional differential systems of neutral type

The purpose of this paper is to obtain oscillation criteria for the differential system $$\begin{gathered} \left[ {y_{\text{1}} \left( t \right) - a\left( t \right)y_{\text{1}} \left( {g\left( t \right)} \right)} \right]^\prime = p\left( t \right)f_1 \left( {y_{\text{2}} \left( {h_2 \left( t \right)} \right)} \right) \hfill {\text{ }}y_2^\prime \left( t \right) = p\left( t \right)f_2 \left( {y_{\text{3}} \left( {h_3 \left( t \right)} \right)} \right) \hfill {\text{ }}y_{\text{3}}^\prime \left( t \right) = - p_3 \left( t \right)f_3 \left( {y_{\text{1}} \left( {h_1 \left( t \right)} \right)} \right),{\text{ }}t \in \mathbb{R}_ + = \left[ {0,\infty } \right) \hfill \end{gathered} $$

Asymptotic stability of differential systems of neutral type

We offer sufficient conditions for the asymptotic stability of the equilibrium point of linear neutral differential systems. An application of our results to a family of artificial neural networks of neutral type is also illustrated.

Waveform Relaxation Methods for Functional Differential Systems of Neutral Type

We investigate continuous-time and discretized waveform relaxation iterations for functional differential systems of neutral type. It is demonstrated that continuous-time iterations converge linearly for neutral equations and superlinearly when the right hand side is independent of the history of the derivative of the solution. The error bounds for discretized iterations are also obtained and some implementation aspects are discussed. Numerical results are presented which indicate a potential speedup of this technique as compared with the classical approach based on discrete variable methods.

Oscillatory properties of functional differential systems of neutral type

Oscillatory properties of functional differential systems of neutral type