Uniform stabilization of Markovian jump linear systems with logarithmic quantization - A convex approach

In this paper, we investigate the almost sure uniform exponential stabilization problem of Markovian jump linear systems (MJLSs) with logarithmically quantized state feedbacks. We introduce the concept and provide explicit constructions of finite path-dependent stabilizing logarithmic quantizers and controllers. We also present a semi-convex algorithm to determine the optimal (coarsest) stabilizing quantization density. As an example, we show that the problem of almost sure uniform stabilization of a linear time-invariant (LTI) system with quantized feedbacks over a lossy channel can be tackled under this framework. A contribution of this work is to provide a systematic approach to simultaneously treat multiple channel constraints in the feedback loop.