Distributed Matrix Pencil Formulations for Prescribed-Time Leader-Following Consensus of MASs With Unknown Sensor Sensitivity

This article investigates the prescribed-time leader-following consensus problem for heterogeneous multiagent systems (MASs) with unknown sensor sensitivity. Considering a connected undirected topology, we introduce a time-varying dual observer/controller design framework that leverages both regular local and inaccurate feedback to achieve consensus tracking within a prescribed time. The proposed analytical framework applies to MASs equipped with sensors exhibiting uncertain sensitivities. A key innovation of our design is the framework of a distributed matrix pencil formulation based on the worst case sensor, leading to control parameters that exhibit sufficient robustness and relatively low conservativeness. Additionally, we establish a bounded time-varying feedback (TVF) scheme that extends the prescribed-time distributed protocol to an infinite time domain without compromising final control accuracy. This includes a detailed discussion of the analytical relationship between switching time and the upper bound of the time-varying gain. In particular, we employ the proportional coefficient obtained from several matrix pencil formulations along with a monotonically increasing time-varying (blow-up) function to derive the feedback gain, simplifying the complexity of control design. Simulations validate the effectiveness of the methodology through a series of electromechanical systems and single-link robot manipulators.