# Asynchronous Non-Fragile H∞ Control for Time-Delay Markovian Jump Singularly Perturbed Systems with Variable Quantization Density and DoS Attack

## TL;DR

This paper proposes a robust control method for complex systems with delays and network issues, ensuring stability and performance.

## Contribution

A novel asynchronous non-fragile H∞ control method is introduced for time-delay Markovian jump systems under quantization and DoS attacks.

## Key findings

- A multi-layer structure method is used to design a non-fragile controller for MJSPSs.
- Mode-dependent Lyapunov–Krasovskii functions ensure stability and H∞ performance under various uncertainties.
- The method's effectiveness is validated using an inverted pendulum system controlled by a DC motor.

## Abstract

This paper investigates the asynchronous non-fragile H∞ control problem for a class of Markovian jump singularly perturbed systems (MJSPSs) with time-varying delays. By applying a multi-layer structure method, a non-fragile controller with time delay is designed for the MJSPSs to adapt to disturbances caused by nonstationary quantization and DoS attacks. To model the asynchronous dynamics between the system and the controller mode, an independent Markov chain is employed to capture the asynchronous quantization and control behavior. By constructing mode-dependent Lyapunov–Krasovskii functions, sufficient conditions are derived to ensure stochastic finite-time exponential stability and H∞ performance under conditions of delay, singular disturbances, and quantization uncertainty. The effectiveness of the method is validated using an inverted pendulum system controlled by a DC motor, demonstrating its ability to achieve robust stability and performance in bandwidth-constrained network environments.