System graph approach to decomposition and decentralised control of LTI interconnected systems

In this paper we use a mesh grid graph representation of general structure LTI systems and introduce an algorithm for full decentralised decomposition of these systems. The algorithm identifies a set of input-output channels that offer strongest combined controllability and observability measures or connectedness. Such decomposition avoids introducing decentralised fixed mode (DFM) and hence ensures existence of stabilisable decentralised output feedback controllers. Once a decentralised decomposition is achieved, we formulate the decentralised controller design as an LMI problem and use existing method to find a feasible solution. A numerical example is given to demonstrate the results of this paper.