Feasibility and Stability Results for Systems with Externally Triggered Switching

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When designing controllers, it is important to consider their stability and safety. However, this can become difficult as the system's complexity increases. This work presents results on the persistent feasibility and stability of externally switching systems. This extends the previous results in the area, which were restricted to narrow classes of systems. The work begins with centralized systems and evolves to explore distributed classes of systems. As with other areas of control system design, distributed methods provide solutions to overcome scaling problems. There are several different tools used in this work to extend the class of systems for which safety and stability assurances can be made. Polytopic sets and their evolution under linear dynamics are used extensively. The parallelization of complex algorithms is another important tool used in these results. Parallelization is a key benefit of distributed systems and prevents the results from falling into the curse of dimensionality. Finally, novel methods of approximating and bounding values are developed, which further reduces the results' numerical complexity. While these approximations do introduce some conservatism, it is often less than the redundancy required in place of formal analysis. The full results of this work advance the study of externally switched systems to applications that, in the past, would not have been possible to study. While fully maturing the field is far too large a goal for any single doctoral dissertation, my contributions include several important advancements that have utility as stand-alone results and provide rich opportunities for future advancements in the field.





Hall, Richard Arlen (2023). Feasibility and Stability Results for Systems with Externally Triggered Switching. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/30259.


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