This paper considers the problem of designing the right-most eigenvalues of linear scalar distributed delay systems using two different but complementary methods: generalized stability charts and matrix Lambert W functions. The generalized stability charts are based on generalized Hopf and fold curves that provide important insight into the problem, but the geometry of the curves may become complicated for certain delay distributions. The Lambert W function approach can be applied to general delay distributions, but requires numerical solutions which can suffer from convergence problems. We present simple examples for both approaches.
- Dynamic Systems and Control Division
Design of Rightmost Eigenvalues Using Distributed Delay
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Wei, F, Orosz, G, & Ulsoy, AG. "Design of Rightmost Eigenvalues Using Distributed Delay." Proceedings of the ASME 2014 Dynamic Systems and Control Conference. Volume 3: Industrial Applications; Modeling for Oil and Gas, Control and Validation, Estimation, and Control of Automotive Systems; Multi-Agent and Networked Systems; Control System Design; Physical Human-Robot Interaction; Rehabilitation Robotics; Sensing and Actuation for Control; Biomedical Systems; Time Delay Systems and Stability; Unmanned Ground and Surface Robotics; Vehicle Motion Controls; Vibration Analysis and Isolation; Vibration and Control for Energy Harvesting; Wind Energy. San Antonio, Texas, USA. October 22–24, 2014. V003T47A003. ASME. https://doi.org/10.1115/DSCC2014-6149
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