Abstract
We clarify, for discrete time systems, two notions of a system with time variant delay, and explore their structural properties. The ultimate purpose is to shed some light on the potential ill-posedness associated with problems with rapidly increasing delay (delay increment greater than one system update step). The main approach is to consider the time delay system using an extension of the state space. For the case of periodically varying delays, this problem becomes a special case of the lifting for periodic systems. Structural problems, such as stability and reachability, can then be investigated using time-invariant theory. For instance, the property that the quotient space of reachable periodic delay systems modulo state space similarity is a smooth manifold, is inherited. A special reflecto-difference equation is analyzed in more detail as an example of a system with unbounded nonlocal behavior.
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Verriest, E.I. (2014). Structure of Discrete Systems with Variable Nonlocal Behavior. In: Vyhlídal, T., Lafay, JF., Sipahi, R. (eds) Delay Systems. Advances in Delays and Dynamics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-01695-5_14
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DOI: https://doi.org/10.1007/978-3-319-01695-5_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01694-8
Online ISBN: 978-3-319-01695-5
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