Conservatism of analysis and controller synthesis of decomposable systems

Recently, distributed controller synthesis approaches for decomposable systems, a subclass of distributed systems with identical subsystems, where the interconnection can be described as LFT interconnection, have been proposed. In order to make these approaches tractable for systems containing a very large number of subsystems, constraints on the Lyapunov matrix and the multiplier matrices are introduced that render the complexity of analysis and controller synthesis smaller and in best case independent on the number of subsystems. Those assumptions have to be paid for with conservatism, which is investigated in this work. It is proven that the conservatism is not reduced if either only the Lyapunov or only the multiplier matrices are constrained, when compared with having constraints on both simultaneously.