Neutral Stochastic Systems Research Articles

Stability and boundedness criteria for certain second-order nonlinear neutral stochastic functional differential equations

This paper presents stochastic stability and stochastic boundedness to certain second-order nonlinear neutral stochastic differential equations. The second-order differential equation is weakened to a neutral stochastic system of first-order equations and used together with a second-order quadratic function to obtain perfect Lyapunov-Krasovskii functional. This functional is adapted and applied to obtain criteria on the nonlinear functions to ensure novel results on stochastic stability and stochastic asymptotic stability of the zero solution. Furthermore, when the forcing term is nonzero, fresh results on stochastic boundedness and uniform stochastic boundedness of solutions are obtained. The results of this paper are original, new, essentially improving, complementing, and simplifying several related ones in the literature. Two special cases of the theoretical results are supplied to demonstrate the applicability of the hypothetical results.

Existence and approximate controllability for the Hilfer fractional neutral stochastic hemivariational inequality with Rosenblatt process

ABSTRACT The approximate controllability of the Hilfer fractional neutral stochastic system with Rosenblatt process is discussed in this article along with the hemivariational inequalities. Initially, we demonstrate the existence of mild solution using fractional calculus, semigroup theory, stochastic analysis, Hilfer fractional derivatives, multivalued maps, and the fixed point theorem. Moreover, we prove the conditions under which the Hilfer fractional system is approximately controllable. Finally, we provide our key findings using an example. Abbreviation: FDEs: Fractional differential equations; R–L: Riemann–Liouville; HF: Hilfer fractional; HFD: Hilfer fractional derivative; SDEs: Stochastic differential equations; HVI: Hemivariational Inequality; HFNSHVI: Hilfer fractional neutral stochastic hemi-variational inequality

T-controllability of higher-order fractional stochastic delay system via integral contractor

The existence, uniqueness and trajectory (T)-controllability results for mild solutions to the fractional neutral stochastic integro-delay differential system are presented in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and sequencing technique. In contrast to previous publications, we do not need to specify the induced inverse of the controllability operator to prove the controllability results, and the relevant non-linear function does not have to meet the Lipschitz condition. Furthermore, T-controllability results for neutral integro-delay differential systems with non-local conditions have been established. Finally, an application to demonstrate the acquired results is discussed.

Stability analysis for neutral stochastic time-varying systems with delayed impulses

This article investigates the stability of stochastic neutral delayed systems (SNDS) with delayed impulses, which includes the stability in input-to-state exponentially stable in pth moment (p-ISES), integral ISES in pth moment (p-iISES) and eλt-weighted ISES in pth moment (eλt-p-ISES). Compared with the existing works, we allow the neutral term, delayed impulses, time-varying coefficients in the diffusion condition, bounded time-varying delay (BTVD) to be in a stochastic system, which arise the difficulty. By utilizing the techniques of Lyapunov-Krasovskii (L-K) function, generalized delay integral inequality and average impulsive interval (AII), some desired results are obtained by surmounting the underlying difficulty. Finally, an example is given to show the validity of our work.

Stability of highly nonlinear neutral stochastic delay system with both stable and unstable subsystems

AbstractThe article addresses the exponentially stable conditions of the highly nonlinear neutral stochastic delayed system (HNNSDS) that contains unstable subsystems apart from stable ones under Markov switching. By the application of the mode‐dependent average dwell time (MDADT) as well as Lyapunov function approach, the general switching condition still satisfies even when the partial Lyapunov coefficients are negative. In addition, the degree of instability is combined with the study of switching signals. On this basis, the case when the system contains only stable subsystems is also investigated. A well‐known switching condition is obtained, establish the foundation of the comparison with more complex cases involving unstable subsystems. The simulation processes are eventually provided to verify rationality of the obtained criteria.

Stability of switched neutral stochastic functional systems with different structures under high nonlinearity

This paper studies the stability of the hybrid neutral stochastic functional differential equations (NSFDEs) with different structures under highly nonlinear conditions. NSFDEs are of wide suitability for simulating random processes with memory, such as tumor evolution mechanism in life science field. The new stochastic system studied in this paper has completely different system structures in different switching subspaces, and the coefficients are highly nonlinear. Moreover, the neutral term is subject to the Markovian switching. This work fills the gap of the stability analysis for differently structured highly nonlinear neutral stochastic functional systems. By using the Lyapunov functional method and the generalized Khasminskii-type conditions, we first establish the existence and uniqueness theorem as well as the asymptotical bounded property of the unique global solution. Then the important stable properties are obtained including H∞ stability, asymptotic stability and exponential stability in Lp. Finally a numerical example is given to illustrate the effectiveness of the results.

On the Asymptotic Stability of Hilfer Fractional Neutral Stochastic Differential Systems with Infinite Delay

On the Asymptotic Stability of Hilfer Fractional Neutral Stochastic Differential Systems with Infinite Delay

Boundedness and stability of nonlinear hybrid neutral stochastic delay differential equation with Lévy jumps under different structures

This paper investigates the boundedness and stability of a class of nonlinear hybrid neutral stochastic differential delay systems with Lévy jumps and different structures. The coefficients in this system satisfy the local Lipschitz condition and a suitable Khasminskii-type condition, and the state space of the system is separated into two subsets, the existence uniqueness, asymptotic boundedness, and exponential stability of the system are obtained by designing a new Lyapunov function and applying the M-matrix technique as well as dealing with the non-differentiable delay function. Different with the existing work, we not only consider the neutral term, but also the case of the delay function being bounded and non-differentiable. At last, numerical examples are performed to manifest the obtained results.

An averaging result for fractional variable-order neutral differential equations with variable delays driven by Markovian switching and Lévy noise

In this paper, we derive new results on the averaging principle for a class of Caputo neutral stochastic system driven by Markovian switching and Lévy noise with variable delays and time-varying fractional order. Under a set of appropriate conditions, we showed that solutions of the averaged stochastic systems approach the solutions of the original stochastic systems in the sense of both convergences in mean square and convergence in probability. Finally, we attach two examples with numerical simulations to justify the validity of our theory.

A note on the general stabilization of discrete feedback control for non-autonomous hybrid neutral stochastic systems with a delay

A note on the general stabilization of discrete feedback control for non-autonomous hybrid neutral stochastic systems with a delay

Approximate controllability of second-order neutral stochastic differential evolution systems with random impulsive effect and state-dependent delay

<p>In this paper, we have discussed a class of second-order neutral stochastic differential evolution systems, based on the Wiener process, with random impulses and state-dependent delay. The system is an extension of impulsive stochastic differential equations, since its random effect is not only from stochastic disturbances but also from the random sequence of the impulse occurrence time. By using the cosine operator semigroup theory, stochastic analysis theorem, and the measure of noncompactness, the existence of solutions was obtained. Then, giving appropriate assumptions, the approximate controllability of the considered system was inferred. Finally, two examples were given to illustrate the effectiveness of our work.</p>

Study approximate controllability and null controllability of neutral delay Hilfer fractional stochastic integrodifferential system with Rosenblatt process

In this paper, we investigate the sufficient conditions for approximate controllability and null controllability of neutral delay stochastic Hilfer fractional integrodifferential system with Rosenblatt process are established. The required results are obtained based on a fixed point technique, fractional calculus and stochastic analysis. Finally, an example is given to illustrate the obtained results.

Boundedness analysis of neutral stochastic systems driven by [formula omitted]-Brownian motion

This paper is concerned with exponential ultimate boundedness problem for a class of neutral stochastic differential systems driven by G-Brownian motion. By developing a method that combines the comparison principle and the reduction to absurdity, we provide sufficient conditions for exponential ultimate boundedness in the mean square of neutral stochastic differential systems driven by G-Brownian motion. The obtained results improve greatly some previous works given in the literature. Finally, some comparisons with existing results and examples are provided to show the effectiveness and superiority of the theoretical results.

Exponential Stability for Second-Order Neutral Stochastic Systems Involving Impulses and State-Dependent Delay

Exponential stability criteria for neutral second-order stochastic systems involving impulses and state-dependent delay have been addressed in this paper based on stability theory, stochastic analysis, and the inequality technique. Some sufficient conditions are given to establish the exponential stability of such systems, which is well-established in the deterministic case, but less known for the stochastic case. In our model, the noise effect can be described as a symmetric Wiener process. By formulating the impulsive integral technique, exponential stability analysis of the pth moment of the second-order system involving stochastic perturbation is established. As an application that illustrates the theoretical formulation, an example is presented.

Stochastic Stabilization of Neutral Stochastic Delay Systems Based on Discrete Observations

Stochastic Stabilization of Neutral Stochastic Delay Systems Based on Discrete Observations

Stabilization of neutral Markovian switching stochastic systems via intermittent noise: A highly nonlinear growth condition

This paper considers the almost surely asymptotic stability of the neutral Markovian switching stochastic systems via periodically intermittent noise. Under the local Lipschitz and highly nonlinear growth conditions, novel sufficient conditions are obtained to ensure the existence and uniqueness of solutions and pth moment boundedness of intermittent stochastic systems. At the same time, by using the Lyapunov function method and M-matrix, it is proved that the system is almost surely asymptotically stable. In addition, the accuracy of the theories is demonstrated by two numerical examples.

Existence and exact controllability results of nonlocal integro-differential neutral stochastic system with finite delay

Existence and exact controllability results of nonlocal integro-differential neutral stochastic system with finite delay

Approximate Controllability Outcomes of Impulsive Second-Order Stochastic Neutral Differential Evolution Systems

In this manuscript, we present a collection of suitable requirements for the approximate controllability outcomes of impulsive second-order stochastic neutral differential evolution systems. We use the ideas from the sine and cosine functions and the fixed point strategy to demonstrate the primary findings. The analysis then moves to second-order nonlocal stochastic neutral differential systems. Eventually, in order to make our topic more useful, we will provide an epistemological implementation.

Optimal control of conformable fractional neutral stochastic integrodifferential systems with infinite delay

The main concern of the manuscript deals with the optimal control problem of conformable fractional neutral stochastic integrodifferential systems with infinite delay. This study is motivated by SAR and RAR systems advantage of providing control over many factors such as power, frequency, phase, polarization, incidence angle, spatial resolution and swath width, all of which are important when designing and operating a radar system. Initially, we investigate the existence of mild solutions for the conformable fractional stochastic integrodifferential equations with infinite delay using stochastic analysis techniques and Banach fixed point theorem. In the later part we establish the existence of mild solutions of the conformable fractional neutral stochastic integrodifferential system with infinite time delay. Furthermore, the existence of optimal control of the corresponding Lagrange optimal control problem is investigated. An example is provided to illustrate the applications of the obtained results. We explain the limitation we have with the existence software, and developed a numerical scheme to justify the theory.

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.