This paper is devoted to stability analysis and synthesis of the linear systems with time-varying delays. Some new stability conditions are developed for the systems based on Lyapunov-Razumikhin theorem. Then a design method for the general state feedback controllers is proposed for the systems with multiple delays by the LMI optimization based approach. Numerical examples are used to demonstra...

This paper is concerned with a leader-following consensus problem for networks of agents with fixed and switching topologies as well as nonuniform time-varying communication delays. By employing Lyapunov-Razumikhin function, a necessary and sufficient condition is derived in the case of fixed topology, and a sufficient condition is obtained in the case when the interconnection topology is switc...

This paper aims to study the existence and global stability of the periodic solutions to time-varying cell neural networks (CNN) with delays. By employing the Lyapunov function and inequality analysis method, the solution to this kind of delay CNN is proved to be bounded and therefore the existence criteria for its periodic solution is established. Moreover, by using Razumikhin technique, the g...

We consider the stability and stabilization of impulsive stochastic delay differential equations ISDDEs . Using the Lyapunov-Razumikhin method, we obtain the sufficient conditions to guarantee the pth moment exponential stability of ISDDEs. Then the almost sure exponential stability is considered and the sufficient conditions of the almost sure exponential stability are obtained. Moreover, the ...

This paper is concerned with the function observer-based stabilization for time-varying delay systems with parameter uncertainties. The uncertain systems tackled in this paper involve uncertainty in quadratic constrained form which includes the well-known normbounded time-varying uncertainty as a special case. In terms of Razumikhin-type stability theorem, we show that the feasibility of severa...

This paper examines the numerical solutions of neutral stochastic functional differential equation. study establishes discrete Razumikhin-type theorem to investigate exponential stability in mean square sense Euler–Maruyama solution this In addition, Borel–Cantelli lemma and analysis theory are incorporated discuss almost sure for such equations.

This paper studies impulsive synchronization of two Lorenz systems. An impulsive control scheme which considers transmission delay in chaos-based secure communication is presented. Sufficient conditions for the globally exponential stabilization of impulsive synchronization of two Lorenz systems are established by employing the Lyapunov-Razumikhin method. Upper bounds of the length and strength...

The global exponential stability problem for a class of switched systems with mixed time delays is investigated in this paper. LMI-based delay-dependent and delay-independent criteria are proposed to guarantee the exponential stability for our considered systems. Razumikhin-like approach and Leibniz-Newton formula are used to find the stability results. Finally, a numerical example is illustrat...

In this present note, we formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via Lyapunov–Razumikhin technique. To demonstrate the developed theory, we conduct stability analyzes for delay sampled-data feed...