We present new methods for proving stability of time-varying linear systems with delays. Our main tools include positive systems and linear Lyapunov functionals. Our work applies to key classes of systems that arise in numerous engineering applications, including neutral systems, and systems that are not necessarily periodic in time and not necessarily positive. We prove stability by comparing the trajectories of the original systems with trajectories of higher dimensional positive systems. One of our key results requires an upper bound on the delay, but the delay can be unknown. Our work also provides robustness of the stability with respect to uncertainties in the coefficient matrices of the system. We illustrate our work in three examples, which show how our methods can sometimes be used with backstepping and linearization to cover even more general classes of systems.
- Dynamic Systems and Control Division
Stability Analysis for Neutral and Time-Varying Systems Using Linear Lyapunov Functionals and a Positive Systems Approach
Mazenc, F, & Malisoff, M. "Stability Analysis for Neutral and Time-Varying Systems Using Linear Lyapunov Functionals and a Positive Systems Approach." 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. V003T47A004. ASME. https://doi.org/10.1115/DSCC2014-6218
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