In this paper, we systematically study the stability of a class of generalized Additive Increase and Multiplicative Decrease/Random Early Detection (AIMD/RED) system. Sufficient conditions are obtained for asymptotic stability of both homogeneous-flow system and heterogeneous-flow system with or without feedback delay by using indirect Lyapunov and Lyapunov–Razumikhin method. Our study reveals ...

Most consensus protocols for Multi-Agent Systems (MAS) presented in the past do not consider communication constraints such as delays in the exchange of information between the agents. In this paper, we provide conditions for a nonlinear, locally passive MAS with timevarying communication delays to reach a consensus, using a recently presented method based on an invariance principle for Lyapuno...

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameters identification and synchronization of uncertain chaotic delayed systems subject to time-varying delay. Firstly, a novel and systematic adaptive scheme of synchronization is proposed for delayed dynamical systems containing uncertainties based o...

In this chapter sufficient conditions for input-to-state stability (ISS) of delayed systems are presented using Lyapunov-Razumikhin functions. It is shown that ISS multistable systems are robust with respect to delays in the feedback path. First, the approach is illustrated by establishing the ISS property for the model of a nonlinear pendulum, then delay-dependent robustness conditions are der...

This paper focuses on the problem of direct adaptive fuzzy control for nonlinear strict-feedback systems with time-varying delays. Based on the Razumikhin function approach, a novel adaptive fuzzy controller is designed. The proposed controller guarantees that the system output converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded...

The object of investigations is a system of impulsive differential equations with “supremum.” These equations are not widely studied yet, and at the same time they are adequate mathematical model of many real world processes in which the present state depends significantly on its maximal value on a past time interval. Practical stability for a nonlinear system of impulsive differential equation...

Robust stability and the guaranteed cost control problem are considered for discrete-time systems with time-varying delays from given intervals. A new construction of Lyapunov– Krasovskii functionals (LKFs), which has been recently introduced in the continuous-time case, is applied. To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the ...