Stabilization of Nonlinear Dynamic Systems Over Limited Capacity Communication Channels

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 erasure channels, respectively, in sure and almost sure senses. The performance of the proposed coding scheme is illustrated by computer simulations.