Leader-follower consensus for linear systems with matched unknown inputs: a fixed-time approach

This study investigates a homogeneous leader-follower multi-agent system with the primary objective of achieving cooperative consensus while simultaneously estimating unknown inputs and states. We propose a novel approach that employs a fixed-time unknown input observer tailored for a general linear case with matched unknown inputs. The observer is constructed using piecewise continuous functions, and we provide the conditions for fixed-time stability. Additionally, the same methodology is applied to establish leader-follower consensus based on the proposed estimator. The fixed-time consensus law is derived under the assumption of zero-error estimation, ensuring effective interaction among the agents. The cooperative dynamics of the multi-agent system enhance the overall performance of the proposed strategies. Numerical simulations are conducted to validate the theoretical analysis, demonstrating the effectiveness and applicability of the proposed methods in practical scenarios.