Dept. of Electrical and Electronic Engineering
The University of Melbourne
It is well-known that the manifestation of time delays in a system can lead to performance degradation and even destabilization of the system, and hence time delay robustness has been a long standing research topic in the systems theory community. While much research has been done and stability criteria have been derived for systems with uncertain constant time-delays, the recent emphasis has been put on the scenario where the time delay is time varying. The significance of such problems is tied to the recent ample interest in designing control algorithms for large-scale networked systems.
Most existing results for checking robust stability of systems with time-varying delays were developed based on the Lyapunov-Razumikhin method or the Lyapunov-Krasovskii. In contrast to the Lyapunov approach, we engage this line of research via a frequency-domain approach called Integral Quadratic Constraint (IQC) Analysis. The advantage of IQC analysis lies in its flexibility. Using this approach, results can be obtained to cope with situations in which time-varying delays, parametric and/or un-modelled dynamical uncertainties, and nonlinear elements such as saturation, relay, hysteresis appear simultaneously.