In this paper the problem of centralized control of a platoon of non-identical vehicles under constant time headway strategy (CTHS) is investigated for multi predecessors following (MPF) topology. A centralized neighbor based linear control law using relative position and velocity is considered for each vehicle. Due to communication and parasitic delays and time-varying network topology, the closed-loop dynamics of platoon is in the form of a multiple delayed switched linear system. New approaches are developed to perform the internal stability analysis of one-dimensional heterogeneous vehicular platoons. Afterwards, sufficient conditions assuring the string stability of a platoon under MPF topology are obtained by presenting a new theorem. In continuance of the paper, some conditions on control parameters guaranteeing safety of the platoon in an emergency braking maneuver are presented through a new theorem. Several simulation results are provided to show the effectiveness of the proposed methods.
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