Input-to-State Stability of Time-Delay Systems: A Link With Exponential Stability

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 input-to-state stability of composite stochastic systems

On input-to-state stability of systems with time-delay: A matrix inequalities approach

Nonlinear matrix inequalities (NLMIs) approach, which is known to be efficient for stability and L2-gain analysis, is extended to input-to-state stability (ISS).We first obtain sufficient conditions for ISS of systems with time-varying delays via Lyapunov–Krasovskii method. NLMIs are derived then for a class of systems with delayed state-feedback by using the S-procedure. If NLMIs are feasible ...

Exponential Stability of Nonlinear Stochastic Systems with Time-delay

This note studies the exponential stability of nonlinear stochastic systems with time delay. Firstly, a more general Lyapunov-Krasovskii functional is constructed, and based on Ito calculus rules for stochastic systems, a novel delay-dependent sufficient condition for exponential stability in mean square is derived in terms of linear matrix inequalities, and it is proved in theory that the obta...

Exponential Stability of Singularly Perturbed Discrete Systems with Time-delay

In this paper, the exponential stability of singularly perturbed discrete systems (SPDSs) with time-delay is investigated via the Lyapunov’s direct method. In the previous results about the SPDS with time-delay, the asymptotic stability is obtained using the frequency-domain approach. However, we propose a composite Lyapunov function to show that the SPDS with time-delay is exponentially stable...