Exponential stability of linear continuous time difference systems with multiple delays

"Some recent results on exponential stability of linear continuous time difference systems with discrete and distributed delay terms are extended to the case of multiple delays. New sufficient conditions for the exponential stability and exponential estimates for the solutions by using Lyapunov–Krasovskii functionals are derived. Special attention is paid to the case of systems with commensurate discrete and distributed delays.

Exponential stability of some linear continuous time difference systems

"In this paper, we consider some classes of linear continuous time difference systems with discrete and distributed delays. For these infinite-dimensional systems, we derive new sufficient delay-dependent conditions for the exponential stability and exponential estimates for the solutions by using Lyapunov-Krasovskii functionals.

Asymptotic behaviour for a class of non-monotone delay differential systems with applications

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family covers a wide set of models used in structured population dynamics. By exploiting the stability and the monotone character of the linear ODE, we establish sufficient conditions for both the extinction of all the populations and the permanence of the system. In the case of DDEs with autonomous coefficients (but possible time-varying delays), sharp results are obtained, even in the case of a reducible community matrix. As a sub-product, our results improve some criteria for autonomous systems published in recent literature. As an important illustration, the extinction, persistence and permanence of a non-autonomous Nicholson system with patch structure and multiple time-dependent delays are analysed.Comment: 26 pages, J Dyn Diff Equat (2017

(R1897) Further Results on the Admissibility of Singular Systems with Delays

Admissibility problem for a kind of singular systems with delays is studied in this article. Firstly, given the singular system with delays is transformed into a neutral system with delays. Secondly, a new sufficient criterion is obtained on the stability of the new neutral system by aid of Wirtinger-based integral inequality, linear matrix inequality (LMI) method and meaningful Lyapunov-Krasovskii functionals (LKFs). This criterion is valid for both systems. At the end, Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB-Simulink software. By this article, we extend and improve some results of the past literature