This work studies certain perturbed and un-perturbed nonlinear systems of continuous discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method Lyapunov–Razumikhin (LRM), uniform asymptotic stability (UAS), (US), integrability boundedness solutions as well exponential (ES) instability are discussed. In this paper, five new theorems a corollary g...

Stability in terms of two measures for nonlinear differential equations with “maxima” is studied. A special type of stability in terms of two measures is defined. The new type of stability generalizes some of the known in the literature. Sufficient conditions for the defined stability are obtained. Cone-valued continuous Lyapunov functions are applied. Method of Razumikhin as well as comparison...

The problem of data packet dropout and transmission delays induced by communication channel in networked control systems (NCSs) is studied in this paper. We model the continuous-time NCSs with data packet dropout and transmission delays as ordinary linear systems with time-varying input delays. By using the Lyapunov–Razumikhin function techniques, delaydependent condition on the stabilization o...

The contribution focuses on the stability analysis of linear time-delay systems within the framework of the Lyapunov – Krasovskii functionals. The method used is based on the idea to check positive definiteness of the functionals exclusively on the specific Razumikhin-type set of functions. For the systems with incommensurate delays, it is proposed to use the modified functionals depend on the ...

In this paper, a robust stabilization problem for a class of linear time-varying delay systems with disturbances is studied using sliding mode techniques. Both matched and mismatched disturbances, involving time-varying delay, are considered. The disturbances are nonlinear and have nonlinear bounds. A sliding surface is designed and the stability of the corresponding sliding motion is analysed ...

When an impulsive control is adopted for a stochastic delay difference system SDDS , there are at least two situations that should be contemplated. If the SDDS is stable, then what kind of impulse can the original system tolerate to keep stable? If the SDDS is unstable, then what kind of impulsive strategy should be taken to make the system stable? Using the Lyapunov-Razumikhin technique, we es...

This paper concerns network congestion control, focusing on a recently proposed “primal-dual” control law that has been shown to give local stability and desirable equilibrium properties for networks of arbitrary capacity and a fixed bound on delay. In this paper we study global stability for these non-linear, delay differential equations, focusing for simplicity on the scenario of a single flo...

The concept of control Lyapunov functions (CLF) has recently been extended to time delay system in the form of control Lyapunov-Razumikhin functions (CLRF) and control Lyapunov-Krasovsky functionals (CLKF). If a CLKF is known for a nonlinear time delay system, several stabilizing control laws can be constructed using one of the universal formulas derived for CLF’s. In this paper we establish a ...