On the instability of differential systems with varying delay

Finite time stabilization of time-delay nonlinear systems with uncertainty and time-varying delay

In this paper, the problem of finite-time stability and finite-time stabilization for a specific class of dynamical systems with nonlinear functions in the presence time-varying delay and norm-bounded uncertainty terms is investigated. Nonlinear functions are considered to satisfy the Lipchitz conditions. At first, sufficient conditions to guarantee the finite-time stability for time-delay nonl...

On exponential stability of nonlinear differential systems with time-varying delay

On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays

In this paper, we propose a new stability criterion for uncertain neutral systems. The considered system has time-varying structured uncertainties and time-varying delay. Based on the Lyapunov method, a delay-dependent criterion for asymptotic stability is derived in terms of LMI (linear matrix inequality). Numerical examples are given to show the effectiveness of our results. 2007 Elsevier Inc...

Delay differential systems with time-varying delay: new directions for stability theory

In this paper we give an example of Markus-Yamabe instability in a constant coefficient delay differential equation with time-varying delay. For all values of the range of the delay function, the characteristic function of the associated autonomous delay equation is exponentially stable. Still, the fundamental solution of the time-varying system is unbounded. We also present a modified example ...

Delay-dependent and delay-independent H∞ control for uncertain neutral differential systems with time-varying delays

In this paper, the H∞ robust control problem for a class of uncertain neutral system with time-varying delays is considered. Based on Lyapunov-Krasovskii functional theory and Leibniz-Newton formula, some criteria for theH∞ robust control with disturbance attenuation are derived. Delay-dependent and delay-independent criteria are proposed to guarantee the stabilization and disturbance attenuati...