Decomposition-Based Distributed Control for Continuous-Time Multi-Agent Systems

In this technical note, we consider the problem of designing distributed controller for a continuous-time system composed of a number of identical dynamically coupled subsystems. The underlying mathematical derivation is based on Kronecker product and a special similarity transformation constructed from interconnection pattern matrix that decomposes the system into modal subsystems. This along with the result of extended linear matrix inequality (LMI) formulation for continuous-time systems makes it possible to derive explicit expressions for computing the parameters of distributed controllers for both static state feedback and dynamic output feedback cases. The main contribution of the technical note is the solution of distributed control problem for continuous-time systems under
H
_∞
/ α-stability and
H
₂
/ α-stability performances by solving a set of LMIs with noncommon Lyapunov variables. The effectiveness of this method is demonstrated by means of a satellite formation example.