Neutral Delay-differential Systems Research Articles

Relative Controllability of ψ-Caputo Fractional Neutral Delay Differential System

The aim of this work is to analyze the relative controllability and Ulamn–Hyers stability of the ψ-Caputo fractional neutral delay differential system. We use neutral ψ-delayed perturbation of the Mitttag–Leffler matrix function and Banach contraction principle to examine the Ulam–Hyers stability of our considered system. We formulate the Grammian matrix to establish the controllability results of the linear fractonal differential system. Further, we employ the fixed-point technique of Krasnoselskii’s type to establish the sufficient conditions for the relative controllability of a semilinear ψ-Caputo neutral fractional system. Finally, the theoretical study is validated by providing an application.

Stability results on random impulsive control for uncertain neutral delay differential systems

This study addresses the delay-dependent criteria like mean square robust exponential stability and mean square exponential stability for the uncertain neutral discrete time-varying and distributed delay differential systems under random impulsive control. By employing the random impulsive control, descriptor model transforms, and Lyapunov functional approach, we achieved the desired performance for the given system in the way of Linear matrix inequality. Finally, we justify the proposed results through numerical examples and their simulations.

Numerical Solutions of a Differential System Considering a Pure Hybrid Fuzzy Neutral Delay Theory

In this paper, we propose and derive a new system called pure hybrid fuzzy neutral delay differential equations. We apply the classical fourth-order Runge–Kutta method (RK-4) to solve the proposed system of ordinary differential equations. First, we define the RK-4 method for hybrid fuzzy neutral delay differential equations and then establish the efficiency of this method by utilizing it to solve a particular type of fuzzy neutral delay differential equation. We provide a numerical example to verify the theoretical results. In addition, we compare the RK-4 and Euler solutions with the exact solutions. An error analysis is conducted to assess how much deviation from exactness is found in the two numerical methods. We arrive at the same conclusion for our hybrid fuzzy neutral delay differential system since the RK-4 method outperforms the classical Euler method.

Analysis of positive fractional-order neutral time-delay systems

In this paper, we consider an initial value problem for linear matrix coefficient systems of the fractional-order neutral differential equations with two incommensurate constant delays in Caputo’s sense. Firstly, we introduce the exact analytical representation of solutions to linear homogeneous and non-homogeneous neutral fractional-order differential-difference equations system by means of newly defined delayed Mittag–Leffler type matrix functions. Secondly, a criterion on the positivity of a class of fractional-order linear homogeneous time-delay systems has been proposed. Furthermore, we prove the global existence and uniqueness of solutions to non-linear fractional neutral delay differential equations system using the contraction mapping principle in a weighted space of continuous functions with regard to classical Mittag–Leffler functions. In addition, Ulam–Hyers stability results of solutions are attained based on fixed-point approach. Finally, we present an example to demonstrate the applicability of our theoretical results.

Results concerning to approximate controllability of non‐densely defined Sobolev‐type Hilfer fractional neutral delay differential system

In this manuscript, our primary focus on the approximate controllability outcomes for non‐densely defined Sobolev‐type Hilfer fractional neutral differential system with infinite delay. By applying the findings and facts associated with fractional theory and the fixed‐point method, the principal discussions are demonstrated. First, we focus on the existence and then discuss the approximate controllability. At last, we provide an example for the demonstration of theory.

Exponential stability of non-linear neutral stochastic delay differential system with generalized delay-dependent impulsive points

This work aims to analyze the exponential stability of a non-linear impulsive neutral stochastic delay differential system. In this study, impulse perturbation is considered a delay-dependent state variable. The solution of the delay-dependent impulsive neutral stochastic delay differential system is associated with the solution of the system without impulses. First, we developed a relation connecting the solution of the neutral stochastic delay differential system without impulses and the solution of the corresponding system with impulses. Then, the conditions of the exponential stability of the proposed impulsive system are derived by determining the stability analysis of the respective system without impulse. The numerical approach for the neutral stochastic delay system without impulses is generated using the Euler-Maruyama method and adopted for the corresponding impulsive system. Finally, the achieved theoretical results are illustrated for applying the Malthusian single species neutral stochastic delay population model with immigration impulses.

Results on controllability of non-densely characterized neutral fractional delay differential system

This work establishes the controllability of nondense fractional neutral delay differential equation under Hille-Yosida condition in Banach space. The outcomes are derived with the aid of fractional calculus theory, semigroup operator theory and Schauder fixed point theorem. Theoretical results are verified through illustration.

Solutions to fractional neutral delay differential nonlocal systems

Abstract The study of neutral fractional delay system governed by nonlocal conditions is presented and proved. With the aid of fractional theory, noncompact measure and Monch’s technique, we established some sufficient conditions to confirm the existence of neutral delay differential system. An illustration of derived results is also offered.

Asymptotic Analysis of Linear and Interval Linear Fractional-Order Neutral Delay Differential Systems Described by the Caputo-Fabrizio Derivative

Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.

Feedback Stabilization of First Order Neutral Delay Systems Using the Lambert W Function

This paper presents a new approach to stabilize the first order neutral delay differential systems with two time delays. First, we provided a few oscillation and non-oscillation criteria for the neutral delay differential equations using spectrum analysis and the Lambert W function. These conditions were explicit and the real roots were analytically expressed in terms of the Lambert W function in the case of non-oscillation. Second, we designed a stabilizing state feedback controller for the neutral delay differential systems with two time delays, wherein the proportional and derivative gains were analytically determined using the results of the non-oscillation criteria. A few examples are given to illustrate the main results.

Oscillation and nonoscillation properties for a kind of nonlinear neutral impulsive delay differential systems

This paper is concerned with oscillation and nonoscillation of a kind of nonlinear neutral impulsive differential systems with constant coefficients and constant delays by using the pulsatile constant. The sufficient and necessary conditions for oscillation in the case δ ∈ R\{0} are obtained. Two examples are included using the main results.

Operational matrix based on Genocchi polynomials for solution of delay differential equations

Abstract In this paper, we present a new simple and effective algorithm for solving generalized Pantograph equations, delay differential equations with neutral terms and delay differential system with constant and variable coefficients.The new method is based on one of the Appell polynomials, namely Genocchi polynomials. We first introduce the properties of Genocchi polynomials and employed them to construct the operational matrices of derivative. Collocation method based on this operational matrix is used. Error estimate for this scheme based on the Generalized pantograph equations is reproduced. Only few terms of Genocchi polynomials are needed to obtain very good results. Numerical examples with comparison show the simplicity, efficiency and accuracy of the method.

Differential Quadrature Method for Stability and Sensitivity Analysis of Neutral Delay Differential Systems

This work develops a computationally efficient stability analysis method for the neutral delay differential systems. This method can be also conveniently applied for the optimal parameter tuning of related control systems. To facilitate this development, at each sampling grid point, the time derivative of the concerned differential system is first estimated by the differential quadrature method (DQM). The neutral delay differential system is then discretized as numbers of algebraic equations in the concerned duration. By combining the obtained discretized algebraic equations, the transition matrix of the two adjacent delay time durations can be explicitly established. Subsequently, the stability boundary is estimated, and the optimal parameters for the controller design are evaluated by searching the global minimum of the spectral radius of the transition matrix. In order to solve such optimization problems with the gradient descent algorithms, this work also analytically formulates the gradient of spectral radius of transition matrix with respect to the concerned parameters. In addition, a strong stability criterion is introduced to ensure better robustness. Finally, the proposed method is extensively verified by numeric examples, and the proposed differential quadrature method demonstrates good accuracy in both parameter tuning and stability region estimation for the neutral delay differential systems.

Improved delay-dependent exponential stability criteria for neutral-delay systems with nonlinear uncertainties

In this paper, the problem of delay-dependent exponential stability criteria for neutral-delay system with nonlinear uncertainties is considered. By constructing a new class of Lyapunov–Krasovskii functionals and using the free-weighting matrices methods within a convex optimization approach, some less conservative delay-dependent stability criteria of neutral delay differential system with nonlinear uncertainties is obtained. These stability conditions are solved as linear matrix inequalities which can be easily solved by various convex optimization algorithms. Finally, numerical examples are given to illustrate the effectiveness of the results.

The stability of distributed neutral delay differential systems with Markovian switching

This paper is concerned with the stability analysis of neutral-type stochastic distributed delay differential systems described by Markovian switching. This system has some special kind of neutral behaviour with uncertain distributed time delays occurring in the state variables. Based on the Lyapunov function, novel methodologies for analyzing stability criteria, and the design of an uncertain distributed delay model are presented. The proposed method is an alternative way to study the robustness and stability of uncertain distributed delays with neutral systems. In order to demonstrate the applicability of the results, the investigation considers two specific examples.

On exponential stability of neutral delay differential system with nonlinear uncertainties

In this paper, the exponential stability for neutral delay differential system with nonlinear uncertainties is investigated. A novel exponential stability criterion for the system is derived using generalized eigenvalue problem (GEVP) approach. Based on this approach, the maximum allowable length and convergence rate is obtained. These stability conditions are formulated as linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms. Numerical examples are given to illustrate the usefulness of our proposed method.

Operational Tau Approximation for Neutral Delay Differential Systems

Operational Tau Approximation for Neutral Delay Differential Systems

Improved observer-based reliable guaranteed cost control for neutral systems

In this note, the problem of observer-based reliable guaranteed cost control for a class of linear neutral delay differential system with actuator failures is investigated. In this paper, some new simple Lyapunov-Krasovskii functionals are constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functionals. Then, using these new simple Lyapunov-Krasovskii functionals, some new delay-dependent stability criteria are derived. It is shown that the system is asymptotically stable against actuator failures if the correspondent sufficient condition can be satisfied. Finally, a numerical example is given to illustrate the effectiveness of the proposed criteria and we can also get information that the guaranteed cost will exist from the example.

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.

Periodicity on a class of neutral impulsive delay system

We present some sufficient conditions for the existence of positive periodic solutions of a class of neutral impulsive delay differential system. When our results applied to the differential system without impulse a known result in the literature is corrected. Moreover, one example is given to illustrate the results obtained.