Stabilization of Markovian Jump Linear Systems With Log Quantized Feedback

Abstract

This paper is concerned with meansquare stabilization of singleinput Markovian jump linear systems (MJLSs) with logarithmically quantized state feedback. We introduce the concepts and provide explicit constructions of stabilizing modedependent logarithmic quantizers together with associated controllers, and a semiconvex 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 timeinvariant (LTI) system over a logquantized erasure channel. A hardware implementation of this application on an inverted pendulum testbed is provided using a finite wordlength approximation.