State feedback control of Markov jump linear systems with hidden-Markov mode observation

TL;DR

This paper develops a unified LMI-based approach for designing state-feedback controllers for Markov jump linear systems with partial, hidden-Markov mode observations, enabling stabilization and $H_2$, $H_ fty$ control.

Contribution

It introduces a generalized LMI framework for control of Markov jump systems with hidden mode observations, extending previous models with perfect, no, or cluster mode information.

Findings

LMI conditions for stabilization and control are derived.

The approach handles various observation scenarios in a unified manner.

Numerical examples demonstrate the effectiveness of the proposed method.

Abstract

In this paper, we study state-feedback control of Markov jump linear systems with partial information. In particular, we assume that the controller can only access the mode signals according to a hidden-Markov observation process. Our formulation generalizes various relevant cases previously studied in the literature on Markov jump linear systems, such as the cases with perfect information, no information, and cluster observations of the mode signals. In this context, we propose a Linear Matrix Inequalities (LMI) formulation to design feedback control laws for (stochastic) stabilization, $H_2$, and $H_\infty$ control of discrete-time Markov jump linear systems under hidden-Markovian observations of the mode signals. We conclude by illustrating our results with some numerical examples.