Key result
An inversion approach exploiting periodicity successfully determined a bounded inverse for general linear periodically time-varying systems.
This paper develops a mathematical inversion approach for linear periodically time-varying systems, though the abstract appears completely unrelated to the cardiology title provided.
May inform periodic signal analysis in cardiology; leaves open clinical validation and application.
Many control applications, including feedforward and learning control, involve the inverse of a dynamical system. For nonminimum-phase systems, the response of the inverse system is unbounded. For linear time-invariant (LTI), nonminimum-phase systems, a bounded, noncausal inverse response can be obtained through an exponential dichotomy. For generic linear time-varying (LTV) systems, such a dichotomy does not exist in general. The aim of this paper is to develop an inversion approach for an important class of LTV systems, namely linear periodically time-varying (LPTV) systems, which occur in, e.g. position-dependent systems with periodic tasks and non-equidistantly sampled systems. The proposed methodology exploits the periodicity to determine a bounded inverse for general LPTV systems. Conditions for existence are provided. Themethod is successfully demonstrated in several application cases, including position-dependent and non-equidistantly sampled systems.
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Ranquin et al. (1977) studied this question. Inversion approach for linear periodically time-varying (LPTV) systems was evaluated. An inversion approach exploiting periodicity successfully determined a bounded inverse for general linear periodically time-varying systems.
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