Construction of continuous abstractions for discrete-time time-delay systems

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.