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Abstract-There has recently been significant interest in feedback stabilization problems with communication constraints including constraints on the available data rate. Signal-to-noise ratio (SNR) constraints are one way in which data-rate limits arise, and are the focus of this paper. In both continuous and discrete-time settings, we show that there are limitations on the ability to stabilize an unstable plant over a SNR constrained channel using finite-dimensional linear time invariant (LTI) feedback. In the case of state feedback, or output feedback with a delay-free, minimum phase plant, these limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity data rate over the same channel. In the case of LTI output feedback, additional limitations are shown to apply if the plant is nonminimum phase. In this case, we show that for a continuous-time nonminimum phase plant, a periodic linear time varying feedback scheme with fast sampling may be used to recover the original SNR requirement at the cost of robustness properties. The proposed framework inherently captures channel noise effects in a simple formulation suited to conventional LTI control performance and robustness analysis, and has potential to handle time delays and bandwidth constraints in a variety of control over communication links problems.

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This paper introduces a novel event-driven sampled-data feedback scheme based on hysteretic quantization. In the proposed sampling scheme, the plant output samples are triggered by the crossings-with hysteresis-of the signal through its quantization levels. The plant and controller communicate over binary channels that operate asynchronously and are assumed to be error and delay-free. The paper proposes two systematic output feedback control design strategies. The first strategy consists in the digital emulation of a previously designed analog controller. If such analog controller achieves closed-loop asymptotic stability, the proposed emulation design guarantees closed-loop practical stability of the resulting asynchronous sampled-data system. The second design strategy is a simple direct design that drives the plant state to the origin in finite time after a total transmission of 2n + 2 bits, where n is the order of the plant. These results exhibit the potential of the proposed scheme for the development of general tools for the analysis and design of practical event-driven sampled-data control systems.