Stabilization of feedback control systems over signal-to-noise ratio constrained channels

In this paper, we study feedback stabilization of a linear time-invariant (LTI) multi-input/multi-output (MIMO) discrete-time system with information constraints in both the input and output channels, characterized by the additive white Gaussian noise (AWGN). A signal-to-noise ratio (SNR) constraint model is adopted in studying its communication capacity limits for the underlying MIMO feedback control system. It has been proven that the computation of the minimum channel capacity is equivalent to a constrained ℋ₂ control problem. We propose an iterative algorithm to compute the required channel capacity for MIMO feedback stabilization and the corresponding MIMO stabilizing feedback controller. The convergence of the proposed iterative algorithm is shown and demonstrated by a numerical example.