相关论文: Spectral Characterizations of Solvability and Stab…

The small-signal stability is an integral part of the power system security analysis. The introduction of renewable source related uncertainties is making the stability assessment difficult as the equilibrium point is varying rapidly. This…

A characteristic matrix function captures the spectral information of a bounded linear operator in a matrix-valued function. In this article, we consider a delay differential equation with one discrete time delay and assume this equation is…

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…

Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the…

A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…

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…

It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…

In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…

The problem of state reconstruction and estimation is considered for a class of switched dynamical systems whose subsystems are modeled using linear differential-algebraic equations (DAEs). Since this system class imposes time-varying…

It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…

Reachability analysis is a fundamental problem for safety verification and falsification of Cyber-Physical Systems (CPS) whose dynamics follow physical laws usually represented as differential equations. In the last two decades, numerous…

In this paper, the stability of IMEX-BDF methods for delay differential equations (DDEs) is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay, $A$ is a positive definite matrix, but $B$ might…

We consider linear systems of equations and inequalities with coefficients varying inside given intervals. We define their solutions (so called AE solutions) and solvability (so called AE solvability) by using forall-exists quantification…

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.

We study an interplay between delay and discontinuous hysteresis in dynamical systems. After having established existence and uniqueness of solutions, we focus on the analysis of stability of periodic solutions. The main object we study is…

We apply parallel approaches in the study of continuous spectra to adiabatic stellar models. We seek continuum eigenmodes for the LAWE formulated as both finite difference and linear differential equations. In particular, we apply methods…

This paper studies stabilities of stochastic differential equation (SDE) driven by time-changed L\'evy noise in both probability and moment sense. This provides more flexibility in modeling schemes in application areas including physics,…

This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…

In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…