Related papers: Strong stability of linear delay-difference equati…
We show how to compose robust stability tests for uncertain systems modeled as linear fractional representations and affected by various types of dynamic uncertainties. Our results are formulated in terms of linear matrix inequalities and…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
Generalized mass-action systems are power-law dynamical systems arising from chemical reaction networks. Essentially, every nonnegative ODE model used in chemistry and biology (for example, in ecology and epidemiology) and even in economics…
We analyse the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. It is well-known that the existence of a positive {\tau} for which the corresponding discrete time…
A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at…
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,…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
For the delayed logistic equation $x_{n+1} = a x_n (a-x_{n-1})$ it is well known that the nontrivial fixed point is locally stable for $1<a\leq 2$, and unstable for $a>2$. We prove that for $1<a\leq 2$ the fixed point is globally stable, in…
The paper presents a new control algorithm for unstable linear systems with input delay. In comparison with known analogues, the control law has been designed, which is a modification of the Smith predictor, and is the simplest one to…
In this paper, a new global exponential stability criterion is obtained for a general multidimensional delay difference equation using induction arguments. In the cases that the difference equation is periodic, we prove the existence of a…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under…
In this paper we prove well-posedness and stabibility of a class of stochastic delay differential equations with singular drift. Moreover, we show local well-posedness under localized assumptions.
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
In this paper, we investigate the rapid stabilizability of linear infinite-dimensional control systems with constant delays. Under the assumptions that the state operator generates an immediately compact semigroup and that the delay…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
The problem of p-th moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii…