Neutral-type Delay Research Articles

Feedback Control Design Strategy for Stabilization of Delayed Descriptor Fractional Neutral Systems with Order 0 < ϱ < 1 in the Presence of Time-Varying Parametric Uncertainty

Descriptor systems are more complex than normal systems, which are modeled by differential equations. This paper derives stability and stabilization criteria for uncertain fractional descriptor systems with neutral-type delay. Through the Lyapunov–Krasovskii functional approach, conditions subject to time-varying delay and parametric uncertainty are formulated as linear matrix inequalities. Based on the established criteria, static state- and output-feedback control laws are designed to ensure regularity and impulse-free properties, together with robust stability of the closed-loop system under permissible uncertainties. Numerical examples illustrate the effectiveness of the control methods and show that the results depend on the range of variation in the delays and on the fractional order, leading to stability analysis results that are less conservative than those reported in the literature.

Smoothness of Solutions to the Damping Problem for Nonstationary Control System with Delay of Neutral Type on the Whole Interval

Smoothness of Solutions to the Damping Problem for Nonstationary Control System with Delay of Neutral Type on the Whole Interval

Smoothness of Solutions to the Damping Problem for Nonstationary Control System with Delay of Neutral Type on the Whole Interval

Smoothness of Solutions to the Damping Problem for Nonstationary Control System with Delay of Neutral Type on the Whole Interval

Stabilization of a nonlinear Euler-Bernoulli viscoelastic beam subjected to a neutral delay

An approach is implemented in this article to analyze the decay rate of nonlinear beams according to the Euler-Bernoulli equation in the context of rheological viscoelastic damping deformations taking into account the neutral type delay. The interaction between viscoelastic and neutral type delays is discussed as our main aim to support a rapidly developing literature. Using the energy method and constructing an appropriate Lyapunov functional, under certain conditions on the kernel and neutral delay terms, we show that despite the destructive nature of delays in general, a very general decaying energy for the problem was obtained.

Distributed model for the drill-string system with multiple regenerative effects in the bit-rock interaction

In this paper, an integrated model is presented to study the axial–torsional dynamics of a distributed drill string. The coupled axial and torsional drill string dynamics typically lead to severe phenomena such as bit-bounce and stick–slip, which are the main causes of failure and efficiency reduction. The top-drive dynamics and the Bottom Hole Assembly (BHA) dynamics are interconnected through the drill pipes. In order to preserve the infinite-dimensional feature of the drill pipes in the mathematical modeling, a distributed model in terms of Delay Differential Algebraic Equations (DDAE) is proposed to represent the dynamics of the drill string. The bit-rock interaction, which consists of the cutting and the frictional components, is responsible for the coupling between the axial and torsional dynamics. A rate-independent bit-rock interaction law is employed for both cutting and frictional components. In order to capture the global bit motion, including multiple regenerative effects, the well-bottom depth function is used to determine the depth of cut. The well-bottom pattern evolution is formulated through algebraic equations rather than Partial Differential Equations (PDEs). A new formulation for the linearized drill string system in terms of Neutral-type Delay Differential Integral Equations (NDDIEs) is proposed to investigate the initiation of the oscillations around the nominal operation. By this formulation, the local stability of the distributed system is studied by determining the right-most eigenvalue of the linearized dynamics. A simulation-based case study reflecting real-life scenarios is presented to investigate the dynamical behavior of the system under different operating conditions.

Finite-Time Synchronization of Complex Networks with Intermittent Couplings and Neutral-Type Delays

Finite-Time Synchronization of Complex Networks with Intermittent Couplings and Neutral-Type Delays

Smoothness of solutions to the damping problem for nonstationary control system with delay of neutral type on the whole interval

We consider the damping problem for a nonstationary control system described by a system of differential-difference equations of neutral type with smooth matrix coe cients and several delays. This problem is equivalent to the boundary-value problem for a system of second-order differentialdifference equations, which has a unique generalized solution. It is proved that the smoothness of this solution can be violated on the considered interval and is preserved only on some subintervals. Su cient conditions for the initial function are obtained to ensure the smoothness of the generalized solution over the entire interval.

Arbitrary decay for a nonlinear Euler-Bernoulli beam with neutral delay

In this paper, the free transverse vibration of a nonlinear Euler- Bernoulli beam under a neutral type delay is considered. In order to suppress the beam transverse vibrations, a boundary control based on the Lyapunov method is designed. The novelty of this paper is the ability to get a wide variety of energy decay rates under free vibration conditions.

GLOBAL WELL-POSEDNESS AND EXPONENTIAL DECAY OF SHEAR BEAM MODEL SUBJECT TO A NEUTRAL DELAY

In this paper, we consider a one-dimensional system known as Shear beam model (no rotary inertia) where the transverse displacement equation is subject to a distributed delay of neutral type. Under some assumptions on the kernel h, we first achieved the global well- posedness of the system by using the classical Faedo-Galerkin approximations along with two a priori estimates. Next, we find the energy expression and by using technique of Lyapunov functional we demonstrate, although delays are known to be of a destructive nature in the general case, that this system is exponentially stable regardless any relationship between coefficients of the system.

Stability test for neutral type delay systems: a piecewise linear approximation scheme*

A necessary and sufficient test for the stability of neutral type linear time-delay systems is presented. Our approach combines the Lyapunov functional expressed in terms of the delay Lyapunov matrix for this class of systems with a piecewise linear approximation of the functional argument. As a result, a stability criterion is given in terms of the non-negative definiteness test of a matrix. An example is presented to validate the obtained result.

On exponential stabilization of a nonlinear neutral wave equation

This work aims to study a nonlinear wave equation subject to a delay of neutral type. The nonlinearity and the delay appear in the second time derivative. In spite of the fact that delays by nature, have an instability effect on the structures, the strong damping is sufficient to allow the system to reach its equilibrium state with an exponential manner. The difficulties arising from the nonlinearity have been overcome by using an inequality due to a Sobolev embedding theorem. The main result has been established without any condition on the coefficient of the neutral delay.

Mittag–Leffler stability and synchronization of neutral-type fractional-order neural networks with leakage delay and mixed delays

In recent years, there have been a lot of studies focusing on the dynamics of fractional-order neural networks (FONNs). One problem is that the standard Lyapunov theory does not apply to fractional-order systems, so these studies rely on the use of Halanay-type lemmas to develop sufficient criteria for certain dynamic properties of FONNs, which frequently results in much more conservative criteria than the ones obtained for integer-order neural networks. The present research uses the Halanay-type lemma in a novel way, in order to obtain less conservative sufficient criteria than previous studies. On the other hand, the previous research only considers FONNs with some types of delays, thus limiting their applicability in real-life scenarios, where possibly many more types of delays are relevant. To address this issue, the paper discusses very general FONNs that include neutral-type delay, leakage delay, time-varying delays, and distributed delay. This is the first time such a general model for the fractional-order scenario has been developed, to our awareness. Three theorems, each based on a distinct Lyapunov-like function, are used to construct sufficient criteria, given in terms of linear matrix inequalities, which ensure, respectively, the Mittag–Leffler stability and synchronization, using two different and general state feedback control schemes, of the proposed networks. The usage of the free weighting matrix approach, among the first times in the context of FONNs, also significantly contributes to reducing the conservatism of the deduced sufficient conditions. One numerical example is provided to illustrate each of the three theorems.

New Delay-Partitioning LK-Functional for Stability Analysis with Neutral Type Systems

This paper investigates the stability issues associated with neutral-type delay systems. Firstly, the delay-partitioning method is employed to construct a brand-new LK-functional candidate. The discrete delay and a neutral delay are divided into several piecewise points through a relaxable sequence of constant numbers, are increasing at a steady rate and are not larger than 1. Secondly, to fully use the interconnection information among the delayed state vectors, a new LK-functional is constructed. Thirdly, the recently published single/multiple integral inequalities are employed to bound the derivative of the newly developed LK function. Finally, a novel stability criterion for neutral systems is developed based on the above treatment. Furthermore, a new corollary is also proposed for the condition of τ=h. The benefits and productivities of our method are demonstrated by numerical examples.

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach

In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional–differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov’s theory. Two application examples verify the analytic findings.

Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems

This paper investigates the stabilization of uncertain neutral-type delay fractional systems. Both static and dynamic output feedback control design methods are proposed. A guaranteed cost-based feedback control design is considered and closed-loop robust stability is investigated using the Lyapunov theorem. Asymptotic stability conditions of the closed-loop system is described in terms of linear matrix inequalities (LMIs). A simulation study, encompassing a numerical example of a fractional order system and a two stage chemical reactor, is considered to assess the performance and validity of the proposed control design.

Lorentz-equivariant flow with four delays of neutral type

We generalize electrodynamics with a second interaction in lightcone. The time-reversible equations for two-body motion define a semiflow on C2(R) with four state-dependent delays of neutral type and nonlinear gyroscopic terms. Furthermore, if the initial segment includes velocity discontinuities, their propagation requires two energetic corner conditions defining boundary layer neighborhoods of large velocities and small denominators. Finally, we discuss a motion restricted to a straight line and a segment pair with vanishing accelerations that iterates to another constant-velocity segment pair.

Dynamical behavior of almost periodically forced neutral delayed equation and its applications

In this paper, we consider a class of almost periodically forced neutral delayed equation, which arises from population model with delays. A threshold parameter in terms of basic reproduction ratio R 0 R_0 is introduced into this neutral system. We derive the strongly subhomonogenous property of skew-product semiflow generated by the linearized neutral system under the assumptions of non-neutral case. We show that the positive almost periodic solution is globally stable by applying the approach of monotone skew-product semiflow. Finally, as a classical example, we illustrate the asymptotic behavior of Nicholson model with neutral type delays by using of the new theoretical results. The dynamical behaviors of neutral delayed equation forced by almost periods in this paper cover automatically some known ones of the non-neutral cases.

Suppression of axial-torsional vibrations of a distributed drilling system by the eigenvector contradiction method

This article proposes an active control strategy to suppress self-excited coupled axial-torsional vibrations of a distributed drill-string system while the coupling takes place through the bit-rock interaction. The drill-string model is expressed as Neutral-type Delay Differential Equations (NDDEs) with constant and state-dependent state delays and constant input delays. As a first step in the novel controller design, an implementable input transformation is introduced, resulting in the elimination of the neutral terms from the equations of motion. This supports a simplified next step of stabilizing controller design. In the second step, a new analytic method named the “Eigenvector Contradiction Method” is proposed to provide sufficient conditions to ensure that all eigenvalues have real parts less than a prescribed value. Based on this criterion, an automated parametric feedback control law is designed. A case study simulation is presented to illustrate the effectiveness of the proposed control strategy.

Combined Nonlinear System of Control of a Structurally-Parametrically Uncertain Nonaffine Plant with State Delay and Neutral Type Delay

Combined Nonlinear System of Control of a Structurally-Parametrically Uncertain Nonaffine Plant with State Delay and Neutral Type Delay

Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation

Stability analysis of uncertain fractional-order neutral-type delay systems with actuator saturation