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In this paper, we derive differential conditions guaranteeing the orbitalstability of nonlinear hybrid limit cycles. These conditions are represented asa series of pointwise linear matrix inequalities (LMI), enabling the search forstability certificates via convex optimization tools such as sum-of-squaresprogramming. Unlike traditional Lyapunov-based methods, the transversecontraction framework developed in this paper enables proof of stability forhybrid systems, without prior knowledge of the exact location of the stablelimit cycle in state space. This methodology is illustrated on a dynamicwalking example.

Transverse Contraction Criteria for Stability of Nonlinear Hybrid Limit Cycles