Neutral Stochastic Systems Research Articles

A stabilization analysis for highly nonlinear neutral stochastic delay hybrid systems with superlinearly growing jump coefficients by variable-delay feedback control

In a recent paper [H. Dong, J. Tang, and X. Mao, SIAM J. Control Optim., 2022], the stability of delayed feedback control of Lévy noise driven stochastic delay hybrid systems is discussed. Notably, the system assumes the absence of the neutral term and imposes the classical linear growth condition on the jump coefficients. This work aims to close the gap by imposing the superlinearly growing jump coefficients for a class of highly nonlinear neutral stochastic delay hybrid systems with Lévy noise (NSDHSs-LN), where neutral-term implies that the systems depend on derivatives with delays in addition to the present and past states. We first show the existence and uniqueness theorem of the solution to the highly nonlinear NSDHSs-LN under the local Lipschitz condition, along with the moment boundedness and finiteness of the solution. We then demonstrate the moment exponential stability and almost sure exponential stability of highly nonlinear NSDHSs-LN through a variable-delay feedback control function and Lyapunov functionals. Finally, we apply our results to a concrete stabilization problem of a coupled oscillator-pendulum system with Lévy noise, and some numerical analyses are presented to illustrate our theoretical results.

Stability Analysis of Time-Varying Neutral Stochastic Hybrid Delay System

Stability Analysis of Time-Varying Neutral Stochastic Hybrid Delay System

Hilfer fractional neutral stochastic Sobolev-type evolution hemivariational inequality: Existence and controllability☆

This paper discusses the approximate controllability of hemivariational inequalities of the Sobolev-type Hilfer fractional neutral stochastic evolution system. Firstly, by using fixed point theorems, fractional calculus, Hilfer fractional derivatives, multivalued maps and stochastic analysis, for stochastic fractional evolution systems, we demonstrate mild solutions. Whereupon we introduce necessary conditions that ensure the approximate controllability of stochastic fractional systems. As a final step, we define our primary outcomes using an example.

Non-Instantaneous Impulsive Fractional Neutral Functional Stochastic Integro-Differential System with Measure of Non-compactness

Non-Instantaneous Impulsive Fractional Neutral Functional Stochastic Integro-Differential System with Measure of Non-compactness

Approximate Controllability of Nonlinear Fractional Stochastic Systems Involving Impulsive Effects and State Dependent Delay

This paper studies the analysis of approximate controllability for the fractional order neutral stochastic impulsive integro-differential systems involving nonlocal condition and State Dependent Delay (SDD). Sufficient conditions are designed to illustrate the evaluation of approximate controllability. It is exhibited that the proposed protocol can explicitly drive the results by Krasnoselskii's fixed point technique and semigroup theory. As a final point, the derived scheme is validated through an example.

Exponential Stability of Fractional Large-Scale Neutral Stochastic Delay Systems with Fractional Brownian Motion

Mathematics plays an important role in many fields of finance. In particular, it presents theories and tools widely used in all areas of finance. Moreover, fractional Brownian motion (fBm) and related stochastic systems have been used to model stock prices and other phenomena in finance due to the long memory property of such systems. This manuscript provides the exponential stability of fractional-order Large-Scale neutral stochastic delay systems with fBm. Based on fractional calculus (FC), Rn stochastic space and Banach fixed point theory, sufficiently useful conditions are derived for the existence of solution and exponential stability results. In this study, we tackle the nonlinear terms of the considered systems by applying local assumptions. Finally, to verify the theoretical results, a numerical simulation is provided.

Asymptotic stability of neutral stochastic pantograph systems with Markovian switching

ABSTRACT This paper investigates the asymptotic stability of neutral stochastic pantograph systems with Markovian switching (NSPSMS). The stochastic LaSalle theorem has been set up to locate the attractive sets for NSPSMS without linear growth condition. Subsequently, combining the stochastic LaSalle theorem and uniformly continuous theory, almost surely asymptotic stability and pth moment asymptotic stability are analysed. Furthermore, we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS, where the coefficients of the delay term are time invariable. Finally, three examples are provided to exhibit the efficiency of the proposed results.

On ν-Level Interval of Fuzzy Set for Fractional Order Neutral Impulsive Stochastic Differential System

The main concern of this paper is to investigate the existence and uniqueness of a fuzzy neutral impulsive stochastic differential system with Caputo fractional order driven by fuzzy Brownian motion using fuzzy numbers with bounded ν-level intervals that are convex, normal and upper-semicontinuous. Fuzzy Itô process, Grönwall’s inequality and the Banach fixed-point theorem are employed to probe the local and global existence. An analytical example is provided to examine the theoretical results.

Trajectory control and [formula omitted]th moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process

The purpose of this paper is to determine a class of neutral stochastic functional integro-differential system in real separable Hilbert spaces as well as the exponential stability results. The Rosenblatt process acts as the driving force behind the systems. Initially, the existence results for mild solutions of the stochastic system is investigated by using stochastic analysis, integro-differential theory, and fixed point theory. The analysis of the exponential stability of mild solutions to nonlinear neutral stochastic integro-differential systems driven by Rosenblatt process is the main objective of the investigation’s further stages. The system’s trajectory controllability is then examined using Gronwall’s inequality. An example is given to validate the results at the end. Our work extends the work of Chalishajar et al. (2010), Chalishajar and Chalishajar (2015), Chalishajar et al. (2023), Muslim and George (2019) and Durga et al. (2022) where the pth moment exponential stability has not discussed. Also, numerical simulation has not studied in Chalishajar et al. (2023), Muslim and George (2019) and Durga et al. (2022).

Approximate controllability of Atangana-Baleanu fractional neutral delay integrodifferential stochastic systems with nonlocal conditions☆

The study of approximate controllability results ensures the essential conditions required for a solution. Keeping the importance of the study, we initiate the existence and approximate controllability an Atangana-Baleanu-Caputo (ABC)-fractional order neutral delay integrodifferential stochastic systems with nonlocal conditions. For this purpose, the suggested ABC-fractional order neutral integrodifferential stochastic system is transferred into an equivalent fixed point problem via an integral operator. The operator is then analyzed for boundedness, continuity and equicontinuity. Then Arzela-Ascolli theorem ensures the compact multivalued function of the operator and Martelli’s fixed point theorem is utilized for the existence of the mild solution. Based on the fixed point theorem and Dunford-Pettis theorem joined with ζ -resolvent operators, we develop the approximate controllability results. Finally, an example is given to justify the theoretical results. The achieved results reveal that the proposed method is systematic and suitable for dealing with the stochastic fractional problems arising in physics, technology, and engineering in terms of the ABC fractional derivative.

Aperiodically Intermittent Control of Neutral Stochastic Delay Systems Based on Discrete Observations

In article, we study the problem of aperiodically intermittent control (APIC) for neutral stochastic delay systems (NSDSs) based on discrete observations. To overcome the difficulty caused by intermittent control, an auxiliary system is introduced. By using the Lyapunov function method, an upper bound of observation period <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta ^{*}$ </tex-math></inline-formula> is obtained. If observation period <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta &lt; \delta ^{*}$ </tex-math></inline-formula> , then the auxiliary system is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(p\geq 2)$ </tex-math></inline-formula> -moment exponentially stable. In addition to the fixed observation period <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta &lt; \delta ^{*}$ </tex-math></inline-formula> , this article gives a method to design an aperiodically intermittent controller and obtains a lower bound of duty cycle for all fixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0 &lt; \underline {T}\leq \overline {T}$ </tex-math></inline-formula> with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\underline {T}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\overline {T}$ </tex-math></inline-formula> being lower bound and upper bound of control frames. That is, we proved the NSDSs with the intermittent discrete observation controller is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(p\geq 2)$ </tex-math></inline-formula> -moment exponentially stable if the auxiliary system is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> th <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(p\geq 2)$ </tex-math></inline-formula> -moment exponentially stable. We call this method the auxiliary system method (ASM). In fact, different from mainstream techniques, the ASM used in this article can handle the case of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0 &lt; \underline {T}\leq \overline {T} &lt; \delta $ </tex-math></inline-formula> even if <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula> is small enough. Besides, this article reveals one interesting phenomenon: classic methods may lead to error accumulation, which cannot be avoided in APIC or periodically intermittent control (PIC) for NSDSs. Finally, one numerical example, one application, and one comparison are given to show the usefulness and correctness of the proposed results.

Existence and approximate controllability results for second-order impulsive stochastic neutral differential systems

This paper focuses on the existence and approximate controllability of second-order non-autonomous impulsive stochastic neutral differential systems in Hilbert spaces. First, by using Schauder's fixed-point theorem, stochastic analysis theory, and evolution operators, a new set of sufficient conditions are formulated, and we prove the existence of mild solutions of second-order non-autonomous impulsive stochastic neutral differential systems. Further, the result is extended to study the approximate controllability results for second-order non-autonomous impulsive stochastic neutral differential systems. Then, a set of sufficient conditions are derived for the approximate controllability of second-order non-autonomous impulsive stochastic neutral differential system by assuming the associated linear system is approximately controllable. The results are obtained with the help of Krasnoselskii's fixed point theorem. Finally, an example is given to illustrate our obtained results.

Delay-dependent Exponential Stability of Linear Stochastic Neutral Systems with General Delays Described by Stieltjes Integrals

Delay-dependent Exponential Stability of Linear Stochastic Neutral Systems with General Delays Described by Stieltjes Integrals

Exponential stabilisation of highly nonlinear neutral stochastic systems by variable-delay feedback control

This paper is devoted to dealing with the exponential stabilisation of highly nonlinear hybrid neutral stochastic differential equation (NSDE) by variable delay feedback control. There have been so far few results on the stabilization of variable delay stochastic systems by variable delay feedback control, although the stabilisation of neutral stochastic systems on the current state has been investigated. Finally, an illustrative example is provided for verifying our theoretical results.

Stabilization of differently structured hybrid neutral stochastic systems by delay feedback control under highly nonlinear condition

This paper mainly studies the stabilization of differently structured highly nonlinear hybrid neutral stochastic systems by delay feedback control. Based on the existing works, our new neutral type stochastic system has completely different highly nonlinear structures in switching subspaces, which is more general and applicable. When such a system is given unstable, we focus on studying the asymptotic and exponential stability criteria by designing a feedback control with a time delay for the underlying system. A simulating example is shown to illustrate the feasibility of these results.

Controllability of retarded time-dependent neutral stochastic integro-differential systems driven by fractional Brownian motion

&lt;p style='text-indent:20px;'&gt;In this manuscript the controllability for a class of time-dependent neutral stochastic integro-differential systems driven by fractional Brownian motion in a separable Hilbert space with delay is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.&lt;/p&gt;

Approximate controllability of neutral fractional stochastic differential systems with control on the boundary

In this paper, the approximate boundary controllability results for neutral fractional stochastic differential system with fractional Brownian motion in Hilbert space is discussed. The existence mild solution of neutral fractional stochastic differential system with fractional Brownian motion is proved by using fractional calculus, compact semigroup, Schauder fixed-point theorem and stochastic analysis. The sufficient conditions for approximate boundary controllability of this system is established under the corresponding linear system is approximately controllable. Finally, an example is given to show the application of our results.

Approximate controllability of Hilfer fractional neutral stochastic systems of the Sobolev type by using almost sectorial operators

&lt;abstract&gt;&lt;p&gt;The main aim of this work is to conduct an analysis of the approximate controllability of Hilfer fractional (HF) neutral stochastic differential systems under the condition of an almost sectorial operator with delay. The theoretical ideas linked to stochastic analysis, fractional calculus and semigroup theory, along with the fixed-point technique, are utilized to establish the key results of this article. More precisely, the main theorem of this study is devoted to proving the fact that the relevant linear system is approximately controllable. Finally, to help this research be as comprehensive as possible, we provide a theoretical application and filter system.&lt;/p&gt;&lt;/abstract&gt;

EXISTENCE AND CONTROLLABILITY FOR IMPULSIVE FRACTIONAL STOCHASTIC EVOLUTION SYSTEMS WITH STATE-DEPENDENT DELAY

This paper is concerned with the impulsive fractional stochastic neutral evolution systems with state-dependent delay and nonlocal condition. First, the existence of solutions of considered evolution systems are obtained by applying the Banach contraction theorem. Then, on the basis of existence of solutions, the controllability concept of the system is investigated. The main aim is to derive some conditions that could be applied to analyze the controllability results for the considered evolution systems involving state-dependent delay. Finally, the efficiency of theoretical analysis is verified by an example.

Exponential stability of delayed neutral impulsive stochastic integro-differential systems perturbed by fractional Brownian motion and Poisson jumps

In this manuscript, we investigate the existence, uniqueness, and exponential stability of a delayed neutral impulsive stochastic integro-differential equation driven by fractional Brownian motion in a separable Hilbert space and Poisson jumps. The results are obtained, using the theory of resolvent operators, stochastic analysis, and a fixed-point technique. Lastly, an example is provided to show the validity of the obtained results.