State-feedback stabilization of Markov jump linear systems with randomly observed Markov states

TL;DR

This paper develops a unified approach using linear matrix inequalities for stabilizing discrete-time Markov jump linear systems with time-randomized Markov state observations, encompassing periodic and renewal-type observations.

Contribution

It introduces a transformation to handle time-randomized Markov observations and proposes a unified LMI-based method for stabilization.

Findings

Effective stabilization method for systems with randomized observations

Handles both periodic and renewal-type observation scenarios

Numerical example demonstrates the approach's viability

Abstract

In this paper we study the state-feedback stabilization of a discrete-time Markov jump linear system when the observation of the Markov chain of the system, called the Markov state, is time-randomized by another Markov chain. Embedding the Markov state into an extended Markov chain, we transform the given system with time-randomized observations to another one having the enlarged Markov-state space but with so-called cluster observations of Markov states. Based on this transformation we propose linear matrix inequalities for designing stabilizing state-feedback gains for the original Markov jump linear systems. The proposed method can treat both periodic observations and many of renewal-type observations in a unified manner, which are studied in the literature using different approaches. A numerical example is provided to demonstrate the obtained result.