Abstract
This paper presents limitations of energy signal-to-noise ratio (SNR) in control of discrete-time linear systems over noisy channels with and without feedback. The minimum SNR required for stabilization is shown to be the modulus of the product of unstable poles of the plants. Two types of optimal control laws that achieve this minimum are constructed based on the gains for expensive control, that is, LQ optimal control without input weight. It is observed that channel feedback does not improve the SNR limitation, which means feedback for control is efficient enough for communication.
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