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Extracting second-order system matrices from state space system

Abstract This technical note concerns the reformation of a second-order system from an arbitrary first-order system. At present, the majority of control literature is concerned with controlling systems within the first-order linearization of a system. The author is part of a growing community looking to expand the direct control of second-order systems and the benefits associated in doing so. However, there are potential stages of system modelling that may result in it being necessary to form the first-order form of the system, such as model reduction. This may have the effect of destroying the second-order notion of the system. The purpose of this note is to regain the structure of the second-order system and thus enable the benefits of direct second-order control to be realized. Although the problem itself has been previously resolved, the author proposes the virtue of a simpler method.