This paper investigates the optimal consensus problem for general linear MASs (of semi-stable and unstable dynamics) subject to control input constraints. The optimal consensus protocols are first designed by inverse optimality approach, based on which the centralized receding horizon control (RHC)-based consensus strategies are designed and the feasibility and consensus properties of the closed-loop systems are analyzed. Utilizing the centralized one, distributed RHC-based consensus strategies are developed. We show that (1) the optimal performance indices under the inverse optimal consensus protocols are coupled with the network topologies and the system matrices of subsystems; (2) the unstable modes of subsystems impose more stringent requirements for the parameter design; (3) the designed RHC-based consensus strategies can make the control input constraints fulfilled and ensure convergent consensus and consensus for MASs with semi-stable and unstable subsystems, respectively. (C) 2018 Elsevier Ltd. All rights reserved.