Linear periodic controller design for decentralized control systems

In the decentralized control of linear time-invariant (LTI) systems, a decentralized fixed mode (DFM) is a system mode which is immoveable using an LTI controller, while a quotient DFM (QDFM) is one which is immoveable using any form of nonlinear time-varying compensation. If a system has no unstable DFMs, there are well-known procedures for designing an LTI stabilizing controller; for systems which have unstable DFMs but no unstable QDFMs, we provide a simple design algorithm which yields a linear periodic sampled-data stabilizing controller.