1,030 Results Found

This paper presents a novel class of conformable integro-differential operators designed to model systems with rapid and ultra-rapid dynamics. This class of local operators enables the design of controllers and observers that induce hyperexponential...

We consider a control system defined by a linear time-varying differential equation of n-th order with uncertain bounded coefficients. The problem of exponential stabilization of the system with an arbitrary given decay rate by linear static state or...

In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponentia...

This paper investigates the problem of rapid exponential stabilization for damped wave equations. Based on a new event-triggered impulsive control (ETIC) method, impulsive control was designed to solve the rapid exponential stabilization of a class o...

This work addresses the problem of globally stabilizing underactuated systems with two inputs and three degrees of freedom. Through appropriate transformations, such dynamics can be expressed as second-order nonholonomic systems in chained form. A ti...

This paper studies the practical exponential stability of an impulsive stochastic food chain system with time-varying delays (ISOFCSs). By constructing an auxiliary system equivalent to the original system and comparison theorem, the existence of glo...

The focus of this work is to investigate the well-posedness and exponential stability of a swelling porous system with the Gurtin–Pipkin thermal effect as the only source of damping. The well-posedness result is achieved using an essential coro...

Incremental stability analysis for time-delay systems has attracted more and more attention for its contemporary applications in transportation processes, population dynamics, economics, satellite positions, etc. This paper researches the criteria fo...

In this paper, we investigate a delayed matrix exponential and utilize it to derive a representation of solutions to a linear nonsingular delay problem with permutable matrices. To begin with, we present a novel definition of $\alpha$-exponential stab...

We provide a sequence of projections on the linear space of all sequences and connect the existence of nonuniform exponential stability to the restrictions of these projections on a class of Banach sequence spaces defined by a discrete dynamics. As a...

In this manuscript, we investigate the exponential stability of a Kirchhoff plate equation with free boundary conditions in a bounded domain of ${\mathbb{R}}^2$. First, we consider the case where the model is subjected only to structural damping and, using the ene...

This paper focuses on the problem of the pth moment and almost sure exponential stability of impulsive neutral stochastic functional differential equations (INSFDEs). Based on the Lyapunov function and average dwell time (ADT), two sufficient criteri...

In this paper, we investigated the stability criteria like an exponential and weakly exponential stable for random impulsive infinite delay differential systems (RIIDDS). Furthermore, we proved some extended exponential and weakly exponential stabili...

For this paper, we consider the almost sure exponential stability of uncertain stochastic Hopfield neural networks based on subadditive measures. Firstly, we deduce two corollaries, using the Itô–Liu formula. Then, we introduce the concep...

This paper focuses on the mean square exponential stability of stochastic delay differential systems with logic impulses. Firstly, a class of nonlinear stochastic delay differential systems with logic impulses is constructed. Then, the logic impulses...

In this paper, we investigate the stability of a 1-d wave equation with boundary difference-type delay control. We utilize the idea of system equivalence to find a system with known stability characteristics and select an appropriate regulation mecha...

In this article, some new sufficient conditions for the exponential stability of nonlinear time-varying delay differential equations are given. An extension of the classical asymptotical stability theorem in terms of a Lyapunov–Razumikhin funct...

This paper examines the numerical solutions of the neutral stochastic functional differential equation. This study establishes the discrete stochastic Razumikhin-type theorem to investigate the exponential stability in the mean square sense of the Eu...

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 co...

The stability analysis of the numerical solutions of stochastic models has gained great interest, but there is not much research about the stability of stochastic pantograph differential equations. This paper deals with the almost sure exponential st...

Regenerative chatter is an unfavorable phenomenon that severely affects machining efficiency and surface finish in milling operations. The prediction of chatter stability is an important way to obtain the stable cutting zone. Based on implicit multis...

In this paper, we present a method to achieve exponential stability in a class of impulsive delayed neural networks containing parameter uncertainties, time-varying delays, and impulsive effect and reaction–diffusion terms. By using an integro-...

This paper is concerned with the problem of dynamic output feedback exponential stability control of T-S fuzzy networked control systems (NCSs) with varying communication delays. First, with consideration of varying communication delays, a new model...

This work establishes an exponential stability result for a porous-elastic system, where the dissipation mechanisms act on the porous and elastic equations. Our result completes some of the results in the literature for unbounded domains.

For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial app...

The stability analysis of Timoshenko beam systems that incorporate delays and fractional boundary controls is a complex area of study in the field of viscoelasticity. Our study aims to balance the symmetric influence of internal viscoelastic damping...

This paper mainly studies the exponential stability of the highly nonlinear hybrid neutral stochastic differential equations (NSDEs) with multiple unbounded time-dependent delays and different structures. We prove the existence and uniqueness of the...

In this paper, we give new sufficient conditions for boundedness and exponential stability of solutions for nonlinear Volterra integro dynamic equations from above on unbounded time scales using first Lyapunovs method. To prove this result we reduce...

This study on the local stability of quaternion-valued neural networks is of great significance to the application of associative memory and pattern recognition. In the research, we study local Lagrange exponential stability of quaternion-valued neur...

This work focuses on a class of stochastic functional differential equations and neutral stochastic differential functional equations. By using a new approach, some sufficient conditions are obtained to guarantee the generalized mean square exponenti...

This paper investigates the global exponential stability of fractional order complex-valued neural networks with leakage delay and mixed time varying delays. By constructing a proper Lyapunov-functional we established sufficient conditions to ensure...

This paper aims to explore the application of sampling control technology in positive Markov jump systems (PMJSs), focusing on the exponential stability in mean and ${\mathcal{L}}_1$-gain performance of the system. We first establish a PMJS model based on sampling...

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...

This work is concerned with the delay-dependent criteria for exponential stability analysis of neutral differential equation with a more generally interval-distributed and discrete time-varying delays. By using a novel Lyapunov–Krasovkii functi...

The global stability of continuous-time multi-input multi-output nonlinear feedback systems with different fractional orders and interval matrices of positive linear parts is investigated. New sufficient conditions for the global stability of this cl...

This paper focuses on the quasi-sure exponential stability of the stochastic differential delay equation driven by G-Brownian motion (SDDE-GBM): $d\xi \left(t\right)=f(t,\xi (t-{\kappa }_1\left(t\right)))dt+g(t,\xi (t-{\kappa }_2\left(t\right)))d\mathcal{Z}\left(t\right),$ where ${\kappa }_1(·),{\&}_{}$...

This paper addresses the robust stabilization problem of a cart–pole system. The controlled dynamics of this interconnected system are deduced by following the analytic framework of Lagrangian mechanics, and the residual terms are formulated as...

In this paper, steady two-dimensional laminar incompressible magnetohydrodynamic flow over an exponentially shrinking sheet with the effects of slip conditions and viscous dissipation is examined. An extended Darcy Forchheimer model was considered to...

This study focuses on the flow of stagnation region and heat transfer of carbon nanotubes (CNTs) over an exponentially stretching/shrinked sheet in the presence of homogeneous–heterogeneous reactions. Kerosene and water are considered base flui...

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Fi...

The existing literature lacks a study on age-dependent population equations based on subadditive measures. In this paper, we propose a hybrid age-dependent population dynamic system (referred to as APDS) that incorporates uncertain random perturbatio...

In this work, a general class of discrete time bidirectional associative memory (BAM) neural networks (NNs) is investigated. In this model, discrete and continuously distributed time delays are taken into account. By utilizing this novel method, whic...

This paper addresses the problem of observer-based control (OBC) for nonlinear systems with time delay (TD). A novel hybrid modeling framework for nonlinear TD systems is first introduced by synergistically combining TD Takagi–Sugeno (TDTS) fuz...

A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water...

This paper considers the exponential stabilization problem for a class of strict-feedback nonlinear systems with multiple time-varying delays, whose nonlinear terms satisfy the linear growth condition. The state feedback controller that relies on a p...

This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems whe...

This paper addresses the stability of stochastic delayed recurrent neural networks (SDRNNs), identifying challenges in existing scalar methods, which suffer from strong assumptions and limited applicability. Three key innovations are introduced: (1)...

This study looks at the stability and stabilization issues concerning the nonlinear time-delay systems specified by conformable derivatives. These requirements can be used for many useful applications. Through the construction of appropriate Lyapunov...

This paper is concerned with stability analysis of discrete-time stochastic delay systems with impulses. By using the sums average value of the time-varying coefficients and the average impulsive interval, two sufficient criteria for exponential stab...

This study presents a comprehensive Lyapunov-based framework for analyzing partial practical stability in nonlinear tempered fractional-order systems (TFOS). We develop novel stability concepts including ${\beta }^{*}$-practical uniform generalized Mittag&n...