Related papers: Stability Results for Systems Described by Coupled…

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

This paper considers a class of space fractional partial differential equations (FPDEs) that describe gas pressures in fractured media. First, the well-posedness, uniqueness, and the stability in $L_(\infty{R})$of the considered FPDEs are…

The paper deals with output feedback stabilization of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic PDE…

The study proposes new results on the set input-to-state stability (ISS) subject to a small input time delay for compact, invariant sets that contains the origin. First, using the nonlinear small-gain theory, we prove a Razumikhin-type…

This paper studies the input-to-state stability (ISS) properties based on the method of Lyapunov functionals for a class of semi-linear parabolic partial differential equations (PDEs) with respect to boundary disturbances. In order to avoid…

The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…

We solve the global asymptotic stability problem of an unstable reaction-diffusion Partial Differential Equation (PDE) subject to input delay and state quantization developing a switched predictor-feedback law. To deal with the input delay,…

Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result…

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…

We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…

Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…

This article introduces and solves a general class of fully coupled forward-backward stochastic dynamics by investigating the associated system of functional differential equations. As a consequence, we are able to solve many different…

This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…

We consider the problem of network stability in finite-buffer systems. We observe that finite buffer may affect stability even in simplest network structure, and we propose an ordinary differential equation (ODE) model to capture the…

Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…

We derive simplified formulas for analyzing the stability of stochastic parametrically forced linear systems. This extends the results in [T. Blass and L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the…

This paper concerns the stability of analytical and numerical solutions of nonlinear stochastic delay differential equations (SDDEs). We derive sufficient conditions for the stability, contractivity and asymptotic contractivity in mean…

This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…

Our general aim is to give sufficient conditions for robustness behavior and convergence to the equilibrium point of linear time-varying fractional system's solutions. We approach this problem using as a framework a series of recent results…

In this paper, we first establish the reflected backward stochastic difference equations with finite state (FS-RBSDEs for short). Then we explore the Existence and Uniqueness Theorem as well as the Comparison Theorem by "one step" method.…