Fixed-time observer-based consensus for linear multi-agent systems with input delay and unknown inputs

This paper addresses the fixed-time leader-follower consensus problem for linear homogenous multi-agent systems subject to simultaneous input delay and unknown inputs, which may be matched or unmatched. A unified observer-based control framework is proposed. First, the Artstein approach is applied to transform the delayed system into a delay-free equivalent. A novel fixed-time unknown input observer is then designed to simultaneously estimate the transformed states and unknown inputs within a bounded time, with sufficient conditions established for its distributed implementation. Based on these estimates, a distributed cooperative control protocol is synthesised to guarantee fixed-time consensus tracking. The overall design ensures that both estimation and consensus are achieved within a fixed settling time, independent of initial conditions. Numerical simulations validate the effectiveness and robustness of the proposed method.