In this work, we establish L2-exponential convergence for a broad class of piecewise deterministic Markov processes recently proposed in the context process Monte Carlo methods and covering particular randomized Hamiltonian (Trans. Amer. Math. Soc. 367 (2015) 3807–3828; Ann. Appl. Probab. 27 (2017) 2159–2194), zig-zag (Ann. Statist. 47 (2019) 1288–1320) bouncy particle Sampler (Phys. Rev. E 85 ...