In this contribution, the estimates for response of time-delay systems with nonlinear homogeneous right-hand side degree strictly greater than one are constructed. The existing results obtained via Lyapunov--Razumikhin approach reminded. Their proofs, revisited in appendix, lead to explicit expressions involved constants. Based on a recently introduced Lyapunov–Krasovskii functional and known d...

Differential equations with impulsive effect provide mathematical models for many phenomena and processes in the field of natural sciences and technology. Recently a well developed stability theory of functional differential systems has come into existence [15-21]. Qualitative properties of impulsive differential equations have been intensively researched for years. In [3-11], by using lyapunov...

This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin Krasovskii approaches, we propose novel control Lyapunov functions/functionals for problem barrier problem. The proposed extend existing ones from delay-free case to case, allow designing stabilizing controllers in closed-form. Since analytical solutions optimal are hard be achiev...

The Liapunov Razumikhin technique is applied to obtain the uniform asymptotic stability for linear integrodifferential equations in Hilbert spaces, x′(t) = A [ x(t) + ∫ t # F (t− s)x(s)ds ] , t ≥ t0 ≥ 0, (# = 0 or −∞), which occur in viscoelasticity and in heat conduction for materials with memory.

At the first time, Razumikhin technique is applied for differential equations with piecewise constant argument of generalized type [1, 2]. Sufficient conditions are established for stability, uniform stability and uniform asymptotic stability of the trivial solution of such equations. We also provide appropriate examples to illustrate our results.

Recommended by Alexander Domoshnitsky By using Lyapunov functions and Razumikhin techniques, the strict stability of impulsive functional differential systems is investigated. Some comparison theorems are given by virtue of differential inequalities. The corresponding theorems in the literature can be deduced from our results.

In the present paper, we study the global stability of sets of sufficiently general type with respect to impulsive functional differential equations with variable impulsive perturbations. The main results are obtained by means of piecewise continuous Lyapunov functions and the use of the Razumikhin technique.

This paper introduces an explicit reference governor approach for controlling time delay linear systems subject to state and input constraints. The proposed framework relies on suitable invariant sets that can be built using both Lyapunov-Razumikhin and LyapunovKrasovskii arguments. The proposed method is validated both numerically and experimentally using several alternative formulations.

© 2012 Manai and Benrejeb, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Robust Stabilization for Uncertain Takagi-Sugeno Fuzzy Continuous Model with Tim...