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In this paper, a serial distributed model predictive control (MPC) approach for connected automated vehicles (CAVS) is developed with local stability (disturbance dissipation over time) and multi-criteria string stability (disturbance attenuation through a vehicular string). Two string stability criteria are considered within the proposed MPC: (i) the l_∞-norm string stability criterion for attenuation of the maximum disturbance magnitude and (ii) l₂-norm string stability criterion for attenuation of disturbance energy. The l_∞-norm string stability is achieved by formulating constraints within the MPC based on the future states of the leading CAV, and the l₂-norm string stability is achieved by proper weight matrix tuning over a robust positive invariant set. For rigor, mathematical proofs for asymptotical local stability and multi-criteria string stability are provided. Simulation experiments verify that the distributed serial MPC proposed …