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This Oxford Seminar features Virginie Debauche discussing "The Path-Complete Formalism for Switched Systems: Stability and Beyond." Explore how switched systems capture complex behaviors involving transitions between different operational modes in modern engineering. Learn about the challenges in analyzing stability in these systems and discover the innovative framework of path-complete Lyapunov functions, which integrates combinatorial structures to represent switching behavior. Understand how this framework combines an automaton (directed graph) encoding admissible switching sequences with a collection of Lyapunov functions to create less conservative stability criteria while reducing combinatorial complexity. See how this approach, originally developed for stability analysis, has expanded to address constrained switching systems, stabilization via switching sequence, control Lyapunov function design, and safety through path-complete barrier functions. Presented on April 17, 2025, this 53-minute seminar from the Topos Institute offers valuable insights into advanced mathematical tools for complex system analysis.
