Improved Robust Stability Bounds for Sampled Data Time Delay Systems

This paper presents improved bounds on the perturbations of continuous time plant matrix for robust stability in a sampled data time delay system framework using discrete Lyapunov stability criterion. The proposed improvement on the bounds is achieved using the state transformations as a vehicle. Several state transformation approaches are explored that result in improved bounds. In addition to the sampling period, time delay induced by the controller (in the form static output feedback) in the network is also incorporated in the analysis via state augmentation. The proposed robustness analysis is carried out for various classes of perturbations such as time invariant perturbations, as well as for structured and unstructured perturbations. The proposed methodologies are illustrated with the help of examples along with a discussion of future research directions in this area.