On infinitesimal contraction analysis for hybrid systems
Provides a theoretical framework for convergence analysis of hybrid systems, which are common in control and robotics, but the results are theoretical without concrete performance numbers.
The paper generalizes infinitesimal contraction analysis to hybrid systems with interacting differential and difference equations, deriving the first contraction results without restrictions on mode sequence or dwell time using an intrinsic distance function.
Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. The technique has primarily been developed for systems governed by a single, possibly nonsmooth, differential or difference equation. We generalize infinitesimal contraction analysis to hybrid systems governed by interacting differential and difference equations. Importantly, we leverage an intrinsic distance function to derive the first contraction results for hybrid systems without restrictions on mode sequence or dwell time. Our theoretical results are illustrated in several examples and applications.