Linear Matrix Inequality‐based design of distributed proportional‐integral‐derivative for the output consensus tracking in heterogeneous high‐order multi‐agent systems

This article addresses the cooperative output consensus tracking problem for high-order heterogeneous multi-agent systems via a distributed proportional-integral-derivative (PID)-like control strategy and proposes two novel control methodologies for the tuning of the control gains, which do not require any assumption and/or limitation on agent system modeling. By extending the static output feedback (SOF) paradigm to distributed domain, the asymptotic stability problem for the overall MAS composed of (Formula presented.) agents is revisited into (Formula presented.) decoupled stabilization problems to be solved. Then, by exploiting the Lyapunov and matrix theory, the typical SOF bilinear matrix inequality (BMI)-based stability conditions are recast into (Formula presented.) feasible linear matrix inequality (LMI)-based ones, whose solutions allow finding the proper values of the PID control gains ensuring the achievement of the cooperative task. In doing so, the proposed procedures reduce the computational effort required for the control design, hence providing a greater attraction for a wider range of practical engineering applications. The scalability and the adaptability of the proposed control methodology in solving an alternative cooperative control problem in the presence of multiple leaders, that is, the output containment task, are also analytically investigated. Numerical simulations confirm the effectiveness of the theoretical derivations.