  In this paper, we derive differential conditions guaranteeing the orbital
stability of nonlinear hybrid limit cycles. These conditions are represented as
a series of pointwise linear matrix inequalities (LMI), enabling the search for
stability certificates via convex optimization tools such as sum-of-squares
programming. Unlike traditional Lyapunov-based methods, the transverse
contraction framework developed in this paper enables proof of stability for
hybrid systems, without prior knowledge of the exact location of the stable
limit cycle in state space. This methodology is illustrated on a dynamic
walking example.
