Related papers: Multi-condition of stability for nonlinear stochas…
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…
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…
In this paper, we investigate the mean-square stabilization for discrete-time stochastic systems that endure both multiple input delays and multiplicative control-dependent noises. For such multi-delay stochastic systems, we for the first…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
In this paper, exponential mean-square stability and almost sure stability of the tamed EM scheme to neutral stochastic differential delay equation are investigated. Surprisingly, the exponential mean-square stability can reproduce the…
In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necessary and sufficient conditions on the forcing terms for…
This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…
In this paper we consider the stability for a type of stochastic McKean-Vlasov equations with non-Lipschitz coefficients. First, sufficient conditions are given for the exponential stability of the second moments for their solutions in…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
We derive a necessary and sufficient condition of linear dynamical stability for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF) model. The condition is expressed by an explicit disequality that has to be…
This note explores the extension of D-stability to non-square matrices, applicable to distributed/decentralized controllability analysis. We first present a definition of D-stability for non-square matrices, directly extending from square…
We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
This paper focuses on the question of how unconditional stability can be achieved via multistep ImEx schemes, in practice problems where both the implicit and explicit terms are allowed to be stiff. For a class of new ImEx multistep schemes…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the…
Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…