MIMO Control Over Additive White Noise Channels: Stabilization and Tracking by LTI Controllers

PROJECT TITLE :

MIMO Control Over Additive White Noise Channels: Stabilization and Tracking by LTI Controllers

ABSTRACT:

During this paper, we study the limitations in stabilization and tracking of multi-input, multi-output (MIMO) networked feedback systems. We have a tendency to adopt a parallel additive white noise (AWN) model for MIMO Communication channels, and contemplate as our performance measure the mean square error for a system's output to track within the mean sq. sense a random reference signal with finite power. We derive necessary and sufficient conditions for the system to be mean square stabilizable and acquire analytical expressions of the optimal performance achievable by linear time-invariant (LTI) controllers subject to channel input power constraint. We have a tendency to show that the AWN channel power constraint imposes elementary limits on the system's stabilizability and tracking performance, that rely on the unstable poles and nonminimum phase zeros of the system. In specific, for MIMO systems, these limits are seen to be enthusiastic about the directions of the unstable poles and nonminimum section zeros, and particularly in how these directions are aligned with noise power distribution; so as to achieve the optimal tracking performance, the channel input power must be allotted to individual channels in ways that accounting for pole/zero directions, a theme that departs from the Shannon's classical “water-filling” strategy. Channel scalings are investigated as a means that of realigning pole/zero directions and redistributing the channel power, which are found to be capable of improving fundamentally a system's stabilizability and tracking performance.

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