This paper describes a new approach to examine the stability of delay differential equations that builds upon prior work using temporal finite element analysis. In contrast to previous analyses, which could only be applied to second order delay differential equations, the present manuscript develops an approach which can be applied to a broader class of systems — systems that may be written in the form of a state space model. A primary outcome from this work is a generalized framework to investigate the asymptotic stability of autonomous delay differential equations with a single time delay. Furthermore, this approach is shown to be applicable to time-periodic delay differential equations and equations that are piecewise continuous.
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A State-Space Temporal Finite Element Approach for Stability Investigations of Delay Equations
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Khasawneh, FA, Mann, BP, & Patel, B. "A State-Space Temporal Finite Element Approach for Stability Investigations of Delay Equations." Proceedings of the ASME 2009 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Volume 1: Active Materials, Mechanics and Behavior; Modeling, Simulation and Control. Oxnard, California, USA. September 21–23, 2009. pp. 415-423. ASME. https://doi.org/10.1115/SMASIS2009-1263
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