Near optimal $$\mathcal {H}_{\infty }$$H∞ performance in the decentralized setting

In this paper, 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 $$H_{\infty }$$H∞-performance criterion in mind. Here we show that if the plant is centrally stabilizable and detectable, the graph associated with the plant is strongly connected, and a technical condition on the relative degree holds, then we can design a decentralized LPC to provide a level of $$H_{\infty }$$H∞ performance as close as desired to that provided by a given (stabilizing) LTI centralized controller; this will be the case even if the plant has an unstable decentralized fixed mode (DFM). This means, in particular, that under the listed conditions, we can design a decentralized LPC to provide near $$H_{\infty }$$H∞-optimal centralized performance.

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