Near Optimal H-Infinity Performance in the Decentralized Setting
In this thesis we consider the use of a linear periodic controller (LPC) for the control of linear time-invariant (LTI) plants in the decentralized setting with an H-infinity performance criterion in mind. If a plant has an unstable decentralized fixed mode (DFM), it is well known that no decentralized LTI controller can stabilize it, let alone provide good performance, which is why we turn to more complicated controllers. Here we show that if the graph associated with the plant is strongly connected and certain technical conditions on the relative degree hold, then we can design a decentralized LPC to provide a level of H-infinity performance as close as desired to the centralized H-infinity optimal performance; this will be the case even if the plant has an unstable DFM. The proposed controller in each channel consists of a sampler, a zero-order-hold, and a discrete-time linear periodic compensator, which makes it easy to implement.