Observer‐Based Containment Control of a Class of Linear‐Varying Multi‐Agent Systems With Disturbances

ABSTRACT This paper presents the first investigation into the exponential containment control problem for a class of general linear time‐varying systems with unmeasurable states and external disturbances. A distributed time‐varying control protocol based on a time‐varying state observer is designed for the scenario of unmeasurable states, achieving exponential convergence for both the state observer and containment control. By employing time‐varying transformations, the observation error system and containment error system are converted into quasi‐linear time‐invariant controllable and observable canonical forms, respectively. Using Lyapunov stability analysis and eigenvalue inequalities, the convergence rate of the observer and the rate at which all followers converge to the convex hull spanned by dynamic leaders are derived. Furthermore, the analysis is extended to systems subjected to exogenous disturbances. A distributed time‐varying control protocol based on a time‐varying state observer and a distributed disturbance observer is proposed, addressing the containment control problem and effectively rejecting disturbances via time‐varying transformations, Lyapunov stability theory, and Young's inequality. Finally, numerical simulations validate the effectiveness and feasibility of the proposed algorithms.