Local Mode Dependent Decentralized $H_{\infty}$ Control of Uncertain Markovian Jump Large-scale Systems

TL;DR

This paper develops a decentralized $H_{ {infty}}$ control approach for large-scale Markov jump systems with uncertainties, using local states and modes, with conditions expressed as rank-constrained LMIs.

Contribution

It introduces a novel decentralized control design method based on local information and rank-constrained LMIs for uncertain Markovian systems.

Findings

Successfully designed controllers satisfying the $H_{ {infty}}$ performance criteria.

Provided a numerical example demonstrating the effectiveness of the proposed method.

Established a new theoretical framework for decentralized control of Markov jump systems.

Abstract

This paper considers the problem of robust $H_{\infty}$ control using decentralized state feedback controllers for a class of large-scale systems with Markov jump parameters. A sufficient condition is developed to design controllers using local system states and local system operation modes. The sufficient condition is given in terms of rank constrained linear matrix inequalities. An illustrative numerical example is given to demonstrate the developed theory.