Improved condition for the optimality of decentralised control for large-scale systems

For a linear constant large-scale system composed for interconnected subsystems, if a decentralised control law which minimises a quadratic cost function with respect to individual decoupled subsystems is used, this simple control strategy is shown to result in a globally optimal interconnected system, provided the condition given by M. Ikeda and D.D. Siljak (1982) is satisfied and the quadratic cost function is modified to include the additional terms arising from the subsystem interactions. An improved condition for the global optimality is given, which implies that, as long as a local eigenvalue condition given in the paper is satisfied for the decentralised local optimal control and the global detectability condition is satisfied, global optimality can also be ensured. It can be expected that, owing to this new simple condition, some of the difficulties in the application of decentralised optimal control approaches could be overcome.