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Tight bound on the stability of control systems over parallel gaussian channels using a new joint source channel coding
, Article 2019 Iran Workshop on Communication and Information Theory, IWCIT 2019, 24 April 2019 through 25 April 2019 ; 2019 ; 9781728105840 (ISBN) ; Motahari, A. S ; Farhadi, A ; Khalaj, B. H ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019
Abstract
In this paper, we address the stability problem of a noiseless linear time invariant control system over parallel Gaussian channels with feedback. It is shown that the eigenvalues-rate condition which has been proved as a necessary condition, is also sufficient for stability over parallel Gaussian channels. In fact, it is proved that for stabilizing a control system over the parallel Gaussian channels, it suffices that the Shannon channel capacity obtained by the water filling technique is greater than the sum of the logarithm of the unstable eigenvalues magnitude. In order to prove this sufficient condition, we propose a new nonlinear joint source channel coding for parallel Gaussian...