Regional consensus of switched positive multi-agent systems with multiple equilibria

This paper investigates regional proportional-integral-derivative consensus of switched positive multi-agent systems with multiple equilibria. A distributed proportional-integral-derivative control protocol is developed by integrating the communication protocol, agent state, and consensus error. A novel switched positive consensus error system is established and analyzed using copositive Lyapunov functions. Subsequently, a Luenberger observer with multiple equilibria is constructed to facilitate the design of an observer-based distributed proportional-integral-derivative control protocol. The regional consensus protocol is designed in the form of linear programming. By employing the proposed protocol, all states of agents are nonnegative and driven into a specific region. The main contributions of the work are summarized as: (i) Construction of a regional proportional-integral-derivative consensus protocol framework for switched positive multi-agent systems with multiple equilibria, (ii) Proposal of an observer-based distributed proportional-integral-derivative control strategy, and (iii) Analysis of the consensus using a matrix decomposition technique, copositive Lyapunov functions, and linear programming. Finally, numerical examples are provided to illustrate the effectiveness of the obtained results.