Robust stability of uncertain time-delay systems

This paper presents several sufficient conditions, delay-independent or delay-dependent, that guarantee the robust stability of uncertain time-delay systems subjected to parametric perturbations. Both single and composite uncertain systems with one delayed state are considered and each of these results, expressed by a succinct scalar inequality, permits the assessment of the transient behaviour of uncertain systems. The robustness of the time-delay system with respect to delay uncertainty is also discussed. Furthermore, these results are extended to the perturbed systems with multiple non-commensurate time delays. It is shown that the parameter perturbations may destabilize the system; hence the nominal system should be sufficiently stable to ensure robust stability.