Inconsistencies in systems with time-varying delays and their resolution

Problems with causality, minimality and inconsistency arise in delay systems when the derivative of the time delay exceeds one. We seek to resolve such problems by proper analysis of the structural properties of a system with time-variant delay and propose new interpretations for such systems, via ‘causalization’: lossless and forgetful. The results are applicable to systems with piecewise constant delays, of interest in control over a network.