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Cyber-Physical Systems (CPSs) require the interfacing of two different time domains: (1) the physical time-continuous domain and (2) the computational time-discrete domain. The Nyquist-Shannon sampling theorem allows transitions from one domain to the other. To preserve the informational signal between both domains, strictly periodic sampling, also known as uniform spaced sampling, is required. CPSs utilise real-time systems to meet temporal constraints. However, real-time systems introduce jitter when several tasks are executed; consequently, the uniform spaced sampling is jeopardized. The Paley-Wiener-Levinson theorem should be used for non-uniform spaced sampling, but its complexity makes it unsuitable for runtime execution in CPSs. Jitter in real-time systems may cause perturbations in CPS applications. In this paper, frequency domain methodologies are proposed to analyse the perturbations introduced by real-time systems in physical applications. It is shown that jitter may introduce frequency components with the potential to jeopardize the dynamics of the physical application. In this paper, it is proposed that jitter should be related to the period of the fundamental frequency to sample, instead of to the period of the real-time task. The frequency domain methodology proposed should be used to analyse the real-time system behaviour from a CPS application point of view.

Analysis of real-time jitter in cyber-physical applications using frequency domain perturbation