Stabilization of Markovian jump linear systems with log-quantized feedback

This paper is concerned with mean-square stabilization of single-input Markovian jump linear systems (MJLSs) with logarithmically quantized state feedback. We introduce the concepts and provide explicit constructions of stabilizing mode-dependent logarithmic quantizers together with associated controllers, and a semi-convex way to determine the optimal (coarsest) stabilizing quantization density. An example application is presented as a special case of the developed framework, that of feedback stabilizing a linear time-invariant (LTI) system over a log-quantized erasure channel. A hardware implementation of this application on an inverted pendulum testbed is provided using a finite word-length approximation.