Distributed H2 control of multi-agent dynamic systems: Continuous-time case

In this paper, we consider the problem of designing distributed controller for a number of identical dynamically coupled agents (vehicles). Under certain structural property associated with state space matrices of these systems, we present a modal decomposition approach that allows the design of distributed controller with H₂ performance. The underlying mathematical derivation is based on Kronecker product and a special similarity transformation constructed from interconnection pattern matrix. This along with the result established for linear matrix inequality (LMI) make it possible to derive explicit expression for computing the parameters of distributed controller for both static state feedback and dynamic output feedback cases. The main contribution of the paper is the solution of distributed control problem for continuous-time systems under H₂ performance by solving a set of LMIs. This set of LMIs enables to design a controller that has the same interconnection structure as the agents. An advantage of this decomposition approach is that the order of computational complexity is reduced by a factor N (the number of agents). The effectiveness of this method is demonstrated by way of a satellite formation example.