The concept of control Lyapunov function has been proven a useful tool for designing robust control laws for nonlinear systems. Recently, this concept has been extended to time-delay systems in the form of Control Lyapunov Razumikhin functions. In this paper we further develop this extension by introducing Control Lyapunov Krasovsky functionals and show their use for robust stabilization of tim...

and Applied Analysis 3 For 0 < q ≤ 1 we have t0D q t x t 1 Γ ( 1 − q d dt (∫ t t0 x s t − s q ds ) , ( 0 < q ≤ 1, c t0D q t x t 1 Γ ( 1 − q ∫ t t0 x′ s t − s q ds, ( 0 < q ≤ 1. 2.2 Some properties of Riemann-Liouville and Caputo derivatives are recalled below 1–3 . Property 1. When 0 < q ≤ 1, we have c t0D q t x t t0D q t x t − x t0 Γ ( 1 − q t − t0 −q. 2.3 In particular, if x t0 0, we have c t...

This paper studies the practical exponential stability of an impulsive stochastic food chain system with time-varying delays (ISOFCSs). By constructing auxiliary equivalent to original and comparison theorem, existence global positive solutions suggested is discussed. Moreover, we investigate sufficient conditions for system, which given by Razumikhin technique Lyapunov method. In addition, whe...

An integro-differential equation is proposed to model a general relapse phenomenon in infectious diseases including herpes. The basic reproduction number R(0) for the model is identified and the threshold property of R(0) established. For the case of a constant relapse period (giving a delay differential equation), this is achieved by conducting a linear stability analysis of the model, and emp...

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

The problem of Impulsive effects on stability analysis of high-order BAM neural networks with time delays is investigated in this paper. By using the Lyapunov technique and Razumikhin method, we characterize theoretically the aggregated effects of impulse and stability properties of impulse-free version and then analyze the stabilizing mechanism and destabilizing mechanism of impulses, strength...

This paper studies the stabilization problem for T-S fuzzy systems with time delay. Based on Lyapunov criterion and Razumikhin theorem, two types of stabilizing controller are designed. One is the linear state feedback controller and the other is the parallel distributed fuzzy controller (PDFC). For each type of the controller, there are some derived sufficient conditions under which the whole ...