Output-based sampled-data control of signed networks via parametric Lyapunov equations approach

This paper is dedicated to demonstrating the influence of leaders on followers in signed networks with antagonistic interactions, where leaders have their own dynamics and interact with other leaders in a strongly connected closed subgraph (SCCC). An output-based distributed sampled-data protocol is designed to comprehensively analyze and assess the impact exerted by leaders on followers, where a heterogeneous sampled-data state observer associated with each agent is developed. The sampled-data control gain is then explicitly calculated via the solutions of parametric Lyapunov equations, enabling more flexible sampling intervals than classical Lyapunov equations. It is demonstrated that leaders in the structurally balanced SCCCs will reach bipartite consensus, and all followers eventually fall within a region that is precisely delineated by the states of these leaders and their corresponding opposite states. For structurally unbalanced graphs, leaders in unbalanced SCCCs reach neutrality, while follower states depend only on leaders in balanced SCCCs. The validity of the theoretical results is verified through simulation tests.