Improved Stability Estimates and Flight Time Predictions Using Higher-Order Transverse Discontinuity Mapping in Hybrid Dynamical Systems

Understand

This article emphasizes on inconsistencies in the dynamical estimates obtained by first-order transverse discontinuity mapping (TDM) and direct numerical observations for hybrid dynamical systems.

• Pitfalls of locally linearizing hybrid nonlinear dynamical systems near discontinuity boundaries are demonstrated along with examples of how such linearization could lead to incorrect estimates of impact occurrences for transverse interactions with a rigid barrier.
• A higher-order TDM is proposed to overcome this shortcoming, allowing for better analytical estimation of impact occurrence times, state transitions, and, consequently, the evolution of trajectories.
• The difference in flight times of two closely initiated trajectories in the local neighbourhood of a discontinuity boundary is estimated up to $\mathcal{O}(2)$.