A lemma of Razumikhin type, pertaining to boundedness of solutions of functional diierential equations, is presented. This lemma is subsequently invoked in the analysis of adaptive strategies that guarantee approximate tracking, with prescribed asymptotic error bound, of reference signals of Sobolev class W 1;1 for two classes of uncertain systems modelled by controlled nonlinear functional dii...

Backstepping design for robust stabilizing control of nonlinear systems with time-delay is investigated in this paper. It is shown that the backstepping design for time-delay systems based on the Lyapunov-Razumikhin function is not a trivial extension of the case of nonlinear nondelay systems due to the existence of the Razumikhin condition. The key point is how to deal with the non-triangular ...

This paper investigates the pth moment globally uniformly exponential stability of a class of impulsive stabilization of stochastic delay differential equations,and the pth moment exponential stability criteria is established by using theLyapunov–Razumikhin method. Keywords—Stochastic delay differential equations; Exponential stability ; Lyapunov-Razumikhin method ; Impulsive control

This paper mainly tends to utilize Razumikhin-type theorems to investigate p-th moment stability for a class of stochastic switching nonlinear systems with delay. Based on the Lyapunov-Razumikhin methods, some sufficient conditions are derived to check the stability of stochastic switching nonlinear systems with delay. One numerical example is provided to demonstrate the effectiveness of the re...

We consider networks of impulsive systems with and without time-delays and investigate under which conditions the whole network is input-to-state stable (ISS). We provide conditions on the size of the time intervals between impulses and on the interconnection structure that guarantee ISS of the overall system, where Lyapunov and Lyapunov-Razumikhin functions for the subsystems are used. The con...

Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochas...

In this article, some new sufficient conditions for the exponential stability of nonlinear time-varying delay differential equations are given. An extension classical asymptotical theorem in terms a Lyapunov–Razumikhin function is obtained. The condition non-positivity time derivative Razumikhin weakened. Additionally, resulting asymptotic allow us to guarantee uniform and evaluate convergence ...

In this paper, we study the problem of hybrid event-triggered control for a class nonlinear time-delay systems. Using Razumikhin-type input-to-state stability result systems, design an algorithm to stabilize given system. order exclude Zeno behavior, combine impulsive mechanism with our strategy. sense, proposed is and Sufficient conditions stabilization systems time delay are obtained by using...

We consider an arbitrary number of interconnected nonlinear systems with time-delays and investigate them in view of input-to-state stability (ISS). The useful tools for single time-delay systems, the ISS Lyapunov-Razumikhin functions and ISS Lyapunov-Krasovskii functionals are redefined and applied to interconnected systems. By the help of a smallgain condition we prove that the whole system w...

In this paper we first study the problem of practical asymptotic stability for a class of discrete-time time-delay systems via Razumikhin-type Theorems. Further the estimations of solution boundary and arrival time of the solution into a region are also investigated based on the practical stability results. Finally, the result on practical asymptotic stability is used to analyze the practical c...