H∞-PID distributed control for output leader-tracking and containment of heterogeneous MASs with external disturbances

This paper addresses both the output leader-tracking and output containment control problems for heterogeneous linear high-order Multi-Agent Systems (MASs) sharing information over a directed communication topology and subject to external unknown disturbances. To solve these control problems, we propose a robust fully distributed Proportional-Integral-Derivative (PID) control strategy, equipped with a filter on the derivative action that allows obtaining both a simpler closed-loop formulation, without the need of the descriptor transformation, and good tracking performances in the case of fast reference signal behaviours. The stability analysis is analytically proven via the Lyapunov theory and the H∞ approach. The derived robust stability conditions are expressed as a set Linear Matrix Inequalities (LMIs) whose solution provides the proper tuning of the robust PID control gains. Numerical simulations confirm the effectiveness and robustness of the proposed approach in solving both the output leader-tracking and output containment control problems.