Synchronization of Multi-Agent Systems with Distributed Reduced Norm State feedback Control

A problem of computing a distributed reduced norm state feedback gain vector that meets a given transient performance specification for synchronization of identical linear time-invariant multi-agent system is considered. The performance specifications impose pole placement constraints on the overall system. Such constraints are non-convex and are converted to convex constraints by using a substitution that linearizes the associated non-linear matrix inequalities. As a result the underlying optimization is reformulated as a semidefinite program (SDP). A solution to the SDP thus obtained, minimizes an upper bound on norm of the gain vector, and thus, reduces the norm of state feedback. Numerical examples demonstrate the effectiveness of the proposed algorithm.