Systems Of Neutral Type Research Articles

Minimax solutions of Hamilton–Jacobi functional equations for neutral-type systems

A functional Hamilton–Jacobi equation with covariant derivatives which corresponds to neutral-type dynamical systems is obtained. The definition of a minimax solution of this equation is given. Conditions under which such a solution exists and is unique and well defined are found.

Necessary Stability Conditions for Neutral Type Systems With a Single Delay

Necessary conditions for the exponential stability of time-delay systems of neutral type, and a new stability criterion for the scalar case are presented in this contribution. They are obtained in the framework of Lyapunov-Krasovskii functionals of complete type. The particularity of these conditions is that they depend exclusively on the delay Lyapunov matrix.

Synchronisation control for neutral-type multi-slave stochastic hybrid systems

ABSTRACTIn this paper, an exponential synchronisation problem for neutral-type multi-slave hybrid systems with stochastic perturbation is discussed, where the adaptive synchronisation model involves a master system and multiple slave systems. By the use of generalised It's formula and M-matrix method, a sufficient condition is obtained to guarantee the stability of the error system, and the update law of the feedback controller is determined to deduce the synchronisation between the master system and the sum system of all slave systems. Finally, a numerical example is given to illustrate the effectiveness of the results obtained in this paper.

A Connection Between Strangeness-Free Delay Differential-Algebraic and Neutral Type Systems

We present an approach that allows to reduce a system of delay differential-algebraic equations to neutral type system with a prescribed additional dynamics. The approach avoids a transformation that divides the system into differential-difference, difference and algebraic parts. We show how the result can be applied to the computation of H2 norm for the delay differential-algebraic system. We assume that the system is strangeness-free that is less conservative than the standard assumption on the delay-free part of the system, which does not take into account the delayed term of the system.

Об уравнении Гамильтона-Якоби-Айзекса-Беллмана для систем нейтрального типа

Об уравнении Гамильтона-Якоби-Айзекса-Беллмана для систем нейтрального типа

Конечномерные аппроксимации конфликтно-управляемых систем нейтрального типа

Конечномерные аппроксимации конфликтно-управляемых систем нейтрального типа

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.

On exponential stability of solutions to periodic neutral-type systems

We consider periodic systems of delay equations. Exponential stability conditions for the zero solution are pointed out by using the Lyapunov-Krasovskiĭ functional. We give some estimates that characterize the decay rate of solutions at infinity.

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.

Stability of neutral type fractional delay systems and its relation with stability of time‐delay and discrete systems

The bounded-input bounded-output stability of fractional delay systems of neutral type is investigated in this study. The proposed method calculates the number of unstable poles of the system for each delay value. All time-delay intervals in time-delay space where system is stable are precisely determined. The stability of systems with not only indefinitely large values of time-delay, but also with multiple poles on the imaginary axis has been studied. The proposed method is employed for investigating the stability of a fractional delay system when its fractional orders approach to the integer numbers or zero. It is proved that simple case of neutral types and time-delay systems have the same conditions for the independent stability. Two numerical examples are provided to illustrate the proficiencies of the proposed method.

Criteria for modal controllability of linear systems of neutral type

For linear autonomous differential-difference systems of neutral type with commensurable delays, we suggest solvability criteria for the modal controllability problem with the use of two classes of state feedback controllers, namely, controllers of constant and variable structure. The proofs are constructive and permit one to obtain the corresponding controllers with the use of standard operations on polynomials and polynomial matrices.

On Exact Controllability of Time-Delay Systems of Neutral Type

Данная работа посвящена решению задачи точной управляемости для достаточно широкого класса систем с запаздыванием нейтрального и смешанного типов. Рассматривая эквивалентную операторную модель в гильбертовом пространстве, мы формулируем условия управляемости в виде некоторой векторной проблемы моментов. Вид данной проблемы моментов существенно упрощается при наличии базиса пространства из собственных векторов оператора системы с запаздыванием. Замена управления позволяет преобразовать структуру системы, и гарантировать существование базиса из собственных векторов соответствующего оператора. Мы доказываем критерий точной управляемости и устанавливаем точное время управления.

Delay and Its Time-Derivative-Dependent Model Reduction for Neutral-Type Control System

This paper is concerned with the problem of model reduction for neutral-type control system. For a given stable neutral-type control system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in a robust performance but is also translated into a linear lower-dimensional system. Sufficient condition is proposed for the asymptotic stability with an error performance for the error system. Then, the model reduction problem is solved by using the projection approach, which casts the model reduction subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, model reduction with special structures is obtained, i.e., no neutral-type model. A numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed controller design approach.

Less-conservative robust adaptive control of neutral systems with mixed time-delays

ABSTRACTIn this paper, the problem of robust stabilisation of a class of neutral-type uncertain linear systems via adaptive control approach is investigated. The neutral systems are assumed to be subjected to model uncertainties, disturbances and mixed time-delays. In comparison to the previous work in the literature, with the assumption that the states of the system and the delayed-states of the system with its derivatives are completely accessible, a new and less-conservative robust adaptive control algorithm is proposed. Based on Lyapunov–Krasovskii function, the model uncertainties and the disturbances are compensated and the stability of the uncertain neutral-type system is guaranteed. The tracking problem via model reference adaptive control is also considered. The most important characteristic of the proposed approach is to make the overall system stability constraints depend on desired arbitrary matrices, and not on the practical system matrices. This is achieved by means of adaptation techniques. Finally, three illustrative examples with numerical simulations are carried out to indicate the significant improvements over some existing results.

Stabilization of retarded systems of neutral type by control Lyapunov–Krasovskii functionals

This paper deals with the stabilization and the practical stabilization of nonlinear systems described by neutral functional differential equations in Hale’s form, affine in the control input. Artstein’s methodology and Sontag’s universal formula are investigated for this class of systems, by means of invariantly differentiable control Lyapunov–Krasovskii functionals.

Predicting the secondary dynamic mode interference phenomenon in thermoacoustic instability control

This paper brings a novel mathematical perspective in assessing the rise of the secondary dynamic modes to prominence during the suppression of thermoacoustic instability. This phenomenon is observed by many earlier investigators; however, without a complete analytical reasoning. We consider a Rijke tube with both a passive Helmholtz resonator and an active feedback control to suppress instabilities. The core dynamics is represented as a linear time-invariant multiple time-delay system of neutral type. Parametric stability of the resulting infinite-dimensional dynamics is investigated using a recent analytical tool: cluster treatment of characteristic roots paradigm. This tool reveals the stability outlook of such systems exhaustively and non-conservatively in the parameter space of the system. First, we examine the stability with and without the Helmholtz resonator. We then select an unstable operation for the resonator-mounted Rijke tube, impose a time-delayed integral feedback control over it and reveal the stabilizing controller parameters using the cluster treatment of characteristic roots methodology. When high control gains are inappropriately selected, the new analytical procedure declares how the secondary dynamic modes of the system exhibit instability although the initially unstable mode is now stabilized. All of these stability assessments are cross-validated using experimental results from a laboratory-scale Rijke tube set-up.

Stability of neutral stochastic switched time delay systems: An average dwell time approach

Summary This paper considers a class of stochastic systems referred to as stochastic switched systems of neutral type with time-varying delay, which combines switched systems with neutral stochastic systems. The systems consist of subsystems of two forms: (i) only stable subsystems and (ii) both stable subsystems and unstable subsystems. By establishing an integral inequality, the exponential stability in pth(p≥1)-moment for such systems with only stable subsystems is first considered. Then, by using an average dwell time approach, the exponential stability in pth(p≥1)-moment for the second form is addressed. An important finding of this study is that when the average dwell time is chosen to be sufficiently large and the total activation time of unstable subsystems is relatively small compared with that of stable subsystems, the exponential stability in pth(p≥1)-moment for such systems can be guaranteed. Two major advantages of these new results are that the differentiability or continuity of the delay function is not required compared with the existing results in the literature, and the proposed approaches can be used to consider the case when the neutral item and the stochastic perturbation are simultaneously presented. An example is provided to verify the effectiveness and potential of the theoretic results obtained. Copyright © 2016 John Wiley & Sons, Ltd.

On the approximation of nonlinear conflict-controlled systems of neutral type

We consider approximations of systems of nonlinear neutral-type equations in Hale’s form by systems of high-order ordinary differential equations. A procedure is given for the mutual feedback tracking between the motion of the original neutral-type conflict-controlled system and the motion of the approximating system of ordinary differential equations. The proposed mutual tracking procedure makes it possible to use approximating systems of ordinary differential equations as finite-dimensional modeling guides for neutral-type systems.

Neimark-Sacker bifurcation analysis in a discrete neutral Nicholson’s blowflies system with delay

In this paper, we investigate the Neimark-Sacker bifurcation in a delayed Nicholson’s blowflies system of neutral type, which is obtained by using Euler discretization method. Choosing time delay as the bifurcation parameter and analysing the associated characteristic equation, we study the stability of the positive equilibrium and verify the existence of the Neimark-Sacker bifurcation. Then, an explicit formula which determines the stability and direction of the bifurcation is given by using centre manifold theorem and normal form theory. Finally, some numerical simulations are given to illustrate our theoretical results.

Estimates for Solutions of One Class of Nonlinear Neutral Type Systems with Several Delays

We consider a class of systems of nonlinear differential equations of neutral type with several delays. We obtain conditions of exponential stability of the zero solution and establish estimates characterizing the exponential decay rate of solutions at infinity. Bibliography: 14 titles.