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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. 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. Here we show that, if the plant is centrally controllable and observable and the graph associated with the plant is strongly connected, then even if the plant has an unstable DFM, we can still design a decentralized LPC to provide LQR performance as close to the centralized optimal performance as desired; 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. [ABSTRACT FROM AUTHOR]

In this technical note we study the servomechanism problem for positive open-loop stable LTI systems under constant tracking signals and constant disturbances. In particular, we show that in general the MIMO servomechanism problem for positive systems is not solvable, but is solvable for various classes of MIMO systems, and for the class of SISO systems in which the disturbances are small compared to the tracking signal. In particular, we give existence results as to what subclass of reference and disturbance signals can be considered, for the case when either the mathematical model of the plant is known or unknown, and we provide the controller structure that solves the problem for the case of measurable or unmeasurable disturbance signals. [ABSTRACT FROM PUBLISHER]