Sharif Digital Repository

This article addresses the stabilization of noiseless nonlinear dynamic systems over limited capacity communication channels. It is shown that the stability of nonlinear dynamic systems over memory-less communication channels implies an inequality condition between the Shannon channel capacity and the summation of the positive equilibrium Lyapunov exponents of the dynamic system or, equivalently, the logarithms of the magnitude of the unstable eigenvalues of system Jacobian. Furthermore, we propose an encoder, decoder, and a controller to prove that scalar nonlinear dynamic systems are stabilizable under the aforementioned inequality condition over the digital noiseless and the packet... 

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...