Moment Exponential Stability Research Articles

STABILITY ANALYSIS FOR STOCHASTIC MCKEAN–VLASOV EQUATION

Abstract The pth ( $p\geq 1$ ) moment exponential stability, almost surely exponential stability and stability in distribution for stochastic McKean–Vlasov equation are derived based on some distribution-dependent Lyapunov function techniques.

Stability, uniqueness and existence of solutions to McKean–Vlasov SDEs: a multidimensional Yamada–Watanabe approach

We establish stability and pathwise uniqueness of solutions to Wiener noise driven McKean–Vlasov equations with random non-Lipschitz continuous coefficients. In the deterministic case, we also obtain the existence of unique strong solutions. By using our approach, which is based on an extension of the Yamada–Watanabe ansatz to the multidimensional setting and which does not rely on the construction of Lyapunov functions, we prove first moment and pathwise exponential stability. Furthermore, Lyapunov exponents are computed explicitly.

Event-triggered impulsive control for nonlinear stochastic delayed systems and complex networks

In this paper, we probe the pth moment exponential stability (p−ES) of stochastic delayed systems subject to event-triggered delayed impulsive control (ETDIC), where the impulsive intensities are assumed to be positive random variables. Based on event-triggered mechanism (ETM) in the sense of expectation, some new sufficient conditions are developed to ensure the stability of the addressed system with Zeno-free behavior. The Lyapunov–Razumikhin method is adopted to handle the time-varying delay in continuous dynamics, and the concept of average random impulsive estimation (ARIE) is introduced to reduce the design requirements of the controller. Especially, the proposed ETDIC strategy not only generates the impulse time sequence according to the predesigned ETM, but also removes the limitations on the size of time delays. Furthermore, the ETM serves as a solution for synchronization problems in complex neural networks. Finally, two examples are given to illustrate the effectiveness of our conclusions.

Stability, Uniqueness and Existence of Solutions to McKean–Vlasov Stochastic Differential Equations in Arbitrary Moments

We deduce stability and pathwise uniqueness for a McKean–Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz continuous drift and includes moment estimates for random Itô processes that are of independent interest. For deterministic coefficients, we provide unique strong solutions even if the drift fails to be of affine growth. The theory that we develop rests on Itô’s formula and leads to pth moment and pathwise exponential stability for p≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\ge 2$$\\end{document} with explicit Lyapunov exponents.

Delay-dependent exponential stability of highly nonlinear stochastic functional switched systems: an average dwell time approach

The delay-dependent exponential stability of stochastic functional switched systems (SFSSs) with highly nonlinear coefficients is investigated in this paper. By virtue of the mode-dependent average dwell time (MDADT) technique, the existence of global solution and qth moment exponential stability is studied without linear growth condition (LGC). Both of drift and diffusion coefficients have functional terms which can embody many existing delay cases, e.g. constant delay, time-varying delay and distributed delay, etc. By employing common/multiple Lyapunov function method, sufficient delay-dependent stability criteria of qth moment exponential stability are proposed. The MDADT condition reveals the positive role of switching signal in the delay-dependent stability analysis. Finally, an example is given to validate our theoretical results.

Stability of highly nonlinear stochastic systems with non-random switching signals and multiple delays

The situation of multiple delays often occur in hybrid stochastic systems. In this paper, multiple time-varying delays are considered for highly nonlinear switching stochastic systems. The function of time-varying delays is differentiable, and its derivative is a positive constant less than 1. By the Lyapunov functional method and the mode-dependent average dwell time approach, existence and uniqueness of solution, asymptotic stability and pth moment exponential stability for highly nonlinear switching stochastic multiple delays systems are obtained. Finally, an example is afforded to explicate the effectiveness our theoretical analysis results.

Integral sliding mode control and stability for Markov jump systems with structured perturbations and time-varying delay driven by fractional Brownian motion

The issues of stability and sliding mode control (SMC) for time-varying delay Markov jump systems (MJSs) with structured perturbations constrained by fractional Brownian motion (fBm) are explored. First, constructing a novel Lyapunov–Krasovskii functional (LKF) with exponential terms that contain the double-integral term, the pth moment exponential stability conditions are derived by utilizing the generalized fractional Itoˆ formula and conditional mathematical expectation. Subsequently, by designing the innovative integral sliding mode surface (SMS) associated with time-varying delay and the SMC law, the state trajectories of the dynamic systems can reach the designed SMS within a finite time. Ultimately, the numerical experiment is executed to confirm and ensure the accuracy and reliability of the obtained results.

Delving a stochastic SEQAIJR COVID-19 model with hexa delayed and copious control strategies

The actual ideal of the literature is to probe the effect of external undulation on prevalence of COVID-19. Owing to some environmental influences, we enhanced our model to the stochastic perturbations. In this article, we scrutinize a stochastic epidemic COVID-19 model with seven states of epidemiological classification. Incipiently, a sophisticated biological system with the effect of time lags put forward copious strategies. At the outset, aim of this work is to explore the existence and uniqueness of global positive solution. Moment exponential stability are upheld. By fabricating a suitable lyapunov function, the sufficient conditions for the persistence of the disease and the existence of an ergodic stationary distribution are established. To regulate the widespread of COVID-19 infection, the main intent is to curb the disease with the succor of three control measures. Finally, the theoretical results bring into being alive in the form of graphical visualization. By nurturing the comparison study, the parameters of the model system come up with real data of most afflicted countries that layout premier consequences.

Exponential stability of impulsive random delayed nonlinear systems with average-delay impulses

In this paper, we investigate the pth moment exponential stability of impulsive random delayed nonlinear systems (RDNS) with average-delay impulses. Utilizing the average impulsive interval, average impulsive delay, and the Lyapunov method, we present several criteria for pth exponential stability in these systems under a novel condition, diverging from previous literature. Additionally, we explore the effects of delayed impulses, analyzing both destabilizing and stabilizing impulses. Our findings reveal the dual effects of time delay in impulses, which can potentially destabilize a stable system or stabilize an unstable one.

Stability of stochastic delayed differential systems with average-random-delay impulses

This paper studies the pth moment exponential stability of stochastic delayed differential systems (SDDSs) with random-delay impulses. By using average random delay (ARD) and average impulsive estimation (AIE) approaches, we obtain a sufficient condition for the pth moment exponentially stable (p-ES) of SDDSs. Compared with some previous results, our work has a wider application since we consider the effects of random factors for systems and impulses. Furthermore, the time delays of the impulses are allowed to be longer than the delay of the system, which shows a big improvement. Finally, the correctness of the results is verified by an example.

Pth Moment Exponential Stability of Impulsive Stochastic Differential Equations with Unbounded Delays

Stochastic impulsive differential equations with Markovian switching have been applied extensively in various areas including ecology systems, neural networks, and control systems, and stability analysis is one fundamental premise of their applications. For two categories of Markovian switched impulsive stochastic differential functional equations with unbounded delays, this paper investigates the pth moment exponential stability by adopting stochastic Lyapunov stability theory and stochastic analysis approach. Several criteria on pth moment exponential stability have been acquired. In the proposed model, the time-varying coefficients and the hybrid impulsive effects are considered simultaneously. It can be seen that the criteria derived in this paper are more concise and the conditions are easier to verify compared with those existing results based on Razumikhin theory. Finally, two examples are illustrated to show the effectiveness of the theoretical findings.

Pth Moment exponential stability of stochastic delayed differential systems with impulsive control involving delays

pth Moment exponential stability of stochastic delayed differential systems with impulsive control involving delays

Analysis and verification of uniform moment exponential stability for stochastic hybrid systems with Poisson jump

Analysis and verification of uniform moment exponential stability for stochastic hybrid systems with Poisson jump

Weak convergence and stability of stochastic hybrid systems with random delay driven by a singularly perturbed Markov chain

This paper focuses on stability of stochastic hybrid systems with random delay driven by a singularly perturbed Markov chain. By weak convergence and the martingale method, the limit system is obtained. Using the limit system as a bridge, this paper establishes the moment exponential stability of the original system by Razumikhin-type techniques. Finally, an example is given to illustrate this result.

Stabilization of hybrid stochastic differential equations with multiple delays via intermittent control

In this paper, we study stability of hybrid stochastic differential equations (SDEs) with multiple delays by intermittent control based on time‐varying delay observations. By constructing an auxiliary non‐delayed hybrid stochastic differential equation and using ‐matrix theory, Lyapunov method, and the comparison principle, sufficient criterions to guarantee the th moment exponential stability and almost sure exponential stability of hybrid SDEs are derived. Finally, a simulation example is shown to illustrate the validity of theoretical results.

Stability of multi-link delayed impulsive stochastic complex networks with Markovian switching

This article presents an analysis of p-th moment exponential stability for a class of stochastic functional differential systems with Markovian switching on complex multi-link networks using multi-delayed impulsive control. The multi-delayed impulsive control scheme implies that the impulsive jumps are related to multiple past states of the systems, which increases the complexity of the analysis. Additionally, single-link networks are extended to complex multi-link networks, which are more extensive. By combining graph theory and the Razumikhin method, several criteria for achieving p-th moment exponential stability for systems are derived. The criteria are related to the maximum upper bound of delays, impulsive interval, and network topology. Subsequently, the stability of multi-link stochastic complex networks with time delays and Markovian switching is studied using delayed impulsive control. Finally, the exponential stability of a class of stochastic coupled multi-link oscillators with Markovian switching is analyzed, and several numerical simulations are provided to verify the validity of the theoretical results.

On exponential stability in [formula omitted]th moment of neutral Markov switched stochastic time-delay systems

In this article, the problem of the pth moment exponential stability is be investigated for neutral Markov switched stochastic time-delay systems. By virtue of inequalities based on the state-dependent multiple Lyapunov functions, we propose adequate conditions for the p-ES of Markov switched neutral stochastic differential delay equation applying properties for the stationary distribution of Markov switched process. For a class of neutral Markov switched stochastic time delay systems with impulse, several new criteria for pth moment exponential stability is obtained using the impulse average dwell-time condition, the integral transformation inequality, and stochastic analysis theory. The results extend and improve the related results from the existing literature. Some examples are provided to illustrate the validity of our derived results.

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.

Some criteria on exponential stability of impulsive stochastic functional differential equations

This paper is mainly concerned with th moment exponential stability of impulsive stochastic functional differential equations. By using the Lyapunov direct method and mathematical induction, we obtain a new generalized impulsive Halanay inequality and some new criteria, which contain two scenarios regarding influence of impulses. On the one hand, when the system itself is unstable, a suitable unidirectional impulse or sequence of impulses can be added to make it stable. On the other hand, we discuss how much impulse perturbation the system can withstand without destabilizing the original system. Finally, two examples are illustrated to show the validity and universality of our results.

Convergence and exponential stability of modified truncated Milstein method for stochastic differential equations

In this paper, we develop a new explicit scheme called modified truncated Milstein method which is motivated by truncated Milstein method proposed by Guo et al. (2018) and modified truncated Euler–Maruyama method introduced by Lan and Xia (2018). We obtain the strong convergence of the scheme under local boundedness and Khasminskii-type conditions, which are relatively weaker than the existing results, and we prove that the convergence rate could be arbitrarily close to 1 under given conditions. Moreover, pth moment exponential stability of the scheme is also obtained Three numerical experiments are offered to support our conclusions.