In this paper, we investigate the problem of global uniform practical exponential stability of a general nonlinear non autonomous differential delay equations. Using the global uniform practical exponential stability of the corresponding differential equation without delay, we show that the differential delay equation will remain globally uniformly practically exponentially stable provided that the time-lag is small enough. Finally, some illustrative examples are given to demonstrate the validity of the results.Mathematics Subject Classification (2010). Primary 93Dxx; Secondary 34Dxx.

In this paper we present a new sufficient condition for absolute stability of delay Lure system. This condition improves the one given in [1]. We use this new criterion to construct an observer‐based control for a class of nonlinear time‐delay systems. Some examples are given to illustrate the results of this paper.

In this paper we deal with a class of uncertain time-varying nonlinear systems with a state delay. Under some assumptions, we construct some stabilizing continuous feedback, i.e. linear and nonlinear in the state, which can guarantee global uniform exponential stability and global uniform practical convergence of the considered system. The quadratic Lyapunov function for the nominal stable system is used as a Lyapunov candidate function for the global system. The results developed in this note are applicable to a class of dynamical systems with uncertain time-delay. Our result is illustrated by a numerical example.

In this paper, we present a new sufficient condition for absolute stability of Lure system with two additive time-varying delay components. This criterion is expressed as a set of linear matrix inequalities (LMIs), which can be readily tested by using standard numerical software. We use this new criterion to stabilize a class of nonlinear time-delay systems. Some numerical examples are given to illustrate the applicability of the results using standard numerical software.

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