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We extend results on backstepping hybrid feedbacks by exploiting synergisticLyapunov function and feedback (SLFF) pairs in a generalized form. Compared toexisting results, we delineate SLFF pairs that are ready-made and do notrequire extra dynamic variables for backstepping. From an (weak) SLFF pair foran affine control system, we construct an SLFF pair for an extended systemwhere the control input is produced through an integrator. The resulting hybridfeedback asymptotically stabilizes the extended system when the synergy gap forthe original system is strictly positive. To highlight the versatility of SLFFpairs, we provide a result on the existence of a SLFF pair whenever a hybridfeedback stabilizer exists. The results are illustrated on the 3D pendulum.

Further results on synergistic Lyapunov functions and hybrid feedback design through backstepping