On Exponential Stability for Linear Difference Equations with Delays

Exponential Stability of Linear Systems with Multiple Time Delays

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new ...

Exponential Stability of Difference Equations with Several Delays: Recursive Approach

On Exponential Stability of Variational Difference Equations

We prove that a general system of variational difference equations is uniformly exponentially stable if and only if certain associated sets are of the second category. We also deduce necessary and sufficient conditions for uniform exponential stability of systems with uniformly bounded coefficients. We apply our results for the study of exponential stability of linear skew-product flows, genera...

Exponential Stability in Nonlinear Difference Equations

Non-negative definite Lyapunov functionals are employed to obtain sufficient conditions that guarantee exponential stability of the zero solution of a nonlinear discrete system. The theory is illustrated with several examples.

New Stability Conditions for Linear Differential Equations with Several Delays

New explicit conditions of asymptotic and exponential stability are obtained for the scalar nonautonomous linear delay differential equation ẋ(t) + m ∑ k=1 ak(t)x(hk(t)) = 0 with measurable delays and coefficients. These results are compared to known stability tests.