Estimation and stability over AWGN channel in the presence of fading, noisy feedback channel and different sample rates

This paper is concerned with estimation and stability of control systems over communication links subject to limited capacity, power constraint, fading, noisy feedback, and different transmission rate rather than system sampling rate. A key issue addressed in this paper is that in the presence of noisy feedback associated with channel, which models transmission of finite number of bits over such links as is the case in most practical scenarios, the well-known eigenvalues rate condition is still a tight bound for stability. Based on an information theoretic analysis, necessary conditions are derived for stability of discrete-time linear control systems via the distant controller in the mean square sense. By construction of a specific coding scheme and by the design of a proper controller, the tight sufficient conditions for stability of control systems are also derived for linear discrete-time control systems over both Additive White Gaussian Noise (AWGN) and fading channels. This implies that the proposed coding scheme is efficient. The results are presented with the mismatch assumption between channel symbol and plant sample rates. As one key result of this paper, it is shown that if the channel symbol rate is less than the system sample rate, the control system is still stabilizable via increasing the transmission power. (C) 2018 Elsevier B.V. All rights reserved.