# Mixed $H_2/H_{\infty}$ Control Control of Delayed Markov Jump Linear Systems

## TL;DR

This paper develops a novel mixed $H_2/H_{
Infty}$ control approach for Markov jump linear systems with state and mode-observation delays, using LMIs for stabilization and control design.

## Contribution

It introduces a remodeling method to handle delays and proposes new LMIs for mixed $H_2/H_{
Infty}$ control of delayed Markov jump systems.

## Key findings

- The proposed LMIs successfully stabilize the system.
- Numerical simulations confirm the effectiveness of the control method.
- The approach handles unknown time-varying delays in control design.

## Abstract

This paper investigates state feedback control laws for Markov jump linear systems with state and mode-observation delays. An assumption in this study is that the delay of mode observation obeys an exponential distribution. Also, we raise an unknown time-varying state delay applied in the composition of the state feedback controller. A method of remodeling the closed-loop system as a standard Markov jump linear system with state delay is shown. Furthermore, on the basis of this remodeling, several Linear Matrix Inequalities (LMI) for designing feedback gains for stabilization and mixed $H_2/H_{\infty}$ control are proposed. Finally, we apply a numerical simulation for examining the effectiveness of the proposed mixed $H_2/H_{\infty}$ controller designing method.