Observer-based bipartite output containment control of heterogeneous multi-agent systems over structurally unbalanced signed graphs

In this paper, we propose state feedback and output feedback observer-based protocols that solve the bipartite output containment (BOC) problem for heterogeneous multi-agent systems over structurally unbalanced signed graphs. The proposed protocols rely solely on the exchange of output information among neighboring agents, resulting in a significant reduction or complete elimination of communication costs. Two design methods for determining controller parameters based on algebraic Riccati equations and linear matrix inequalities (LMIs) are proposed. Each method offers distinct advantages while ensuring that the closed-loop system poles are placed within a predefined region in the complex plane. Furthermore, an extensive solvability analysis is conducted, demonstrating that the solvability of the BOC problem using the proposed approach can be pre-guaranteed for a broad range of agent dynamics.