@inproceedings{9304184, author = {Shahamat, M. and Askari, J. and Swikir, A. and Noroozi, N. and Zamani, M.}, title = {Construction of continuous abstractions for discrete-time time-delay systems}, booktitle = {2020 59th IEEE Conference on Decision and Control (CDC)}, year = {2020}, month = {Dec}, doi = {10.1109/CDC42340.2020.9304184}, abstract = {In this paper we construct continuous abstraction for discrete-time time-delay systems via the notion of so-called Razumikhin simulation functions. We show that the existence of such a function guarantees that the mismatch between the out-put trajectory of the concrete system and that of its abstraction lies within an appropriate bound. By transforming a system with time delay into an interconnected system without time delay, we show that the Razumikhin method is a small-gain type approach for time-delay systems and enables us to effectively manage computational complexity of constructing abstractions. We further extend our approach to compositional construction of large-scale systems containing interconnection and/or local time delays. For linear systems, we provide an algorithmic procedure for compositional construction of abstractions, which is expressed in terms of linear matrix inequalities.}, keywords = {Delay effects;Trajectory;Delays;Interconnected systems;Computational modeling;Linear systems;Stability analysis}, }