Gradient Methods for Fixed Structure Controller Synthesis and System Identification of Decomposable Systems

In this letter we are considering the problem of fixed structure controller synthesis and system identification for large scale systems. The systems considered are referred to as decomposable systems and can be seen as resulting from the interconnection of a large number of identical subsystems. Combining recent results from nonsmooth controller synthesis with the special structure of decomposable systems, we show that the computational complexity of the controller synthesis and system identification procedure scale linearly with the size of the system. Employing results from robust control, the computational complexity of the controller synthesis can be reduced further, however, at the cost of additional conservatism. Using numerical examples we demonstrate that the proposed method can reduce the conservatism compared to existing LMI methods for full order decomposable controllers.