Related papers: On exponential stability for linear discrete-time …
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
Exponential stability of modified truncated Euler-Maruyama method for stochastic differential equations are investigated in this paper. Sufficient conditions for the $p$-th moment and almost sure exponential stability of the given numerical…
We study abstract sufficient criteria for open-loop stabilizability of linear control systems in a Banach space with a bounded control operator, which build up and generalize a sufficient condition for null-controllability in Banach spaces…
We analyze Galerkin discretizations of a new well-posed mixed space-time variational formulation of parabolic PDEs. For suitable pairs of finite element trial spaces, the resulting Galerkin operators are shown to be uniformly stable. The…
Assuming the existence of a general nonuniform dichotomy for the evolution operator of a non-autonomous ordinary linear differential equation in a Banach space, we establish the existence of invariant stable manifolds for the semiflow…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…
The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservation laws, as arises in modern biomorphology models, binary…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
The fundamental Filippov-Wazwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation…
This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in $\mathbb R^d$ ($d\ge3$) with a smooth…
The Markov-Bernstein type inequalities between the norms of functions and of their derivatives are analysed for complex exponential polynomials. We establish a relation between the sharp constants in those inequalities and the stability…
We give a relation between the exponential stability of $ C_{0}- $semigroup $ \textbf{T}=\left\lbrace T(t) \right\rbrace_{t\geq 0} $ and the solutions of Lyapunov inequality \( \left\langle QAx,x\right\langle +\left\langle…
Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…
We present a characterization of $(\mu,\nu)$-dichotomies in terms of the admissibility of certain pairs of weighted spaces for nonautonomous discrete time dynamics acting on Banach spaces. Our general framework enables us to treat various…
We consider the numerical approximation of linear damped wave systems by Galerkin approximations in space and appropriate time-stepping schemes. Based on a dissipation estimate for a modified energy, we prove exponential decay of the…