Asynchronous Non-Fragile H_∞ Control for Time-Delay Markovian Jump Singularly Perturbed Systems with Variable...

Area of Science:

• Control Systems Engineering
• Networked Systems
• Stochastic Systems

Background:

• Markovian jump singularly perturbed systems (MJSPSs) are complex dynamic systems.
• Time-varying delays, nonstationary quantization, and denial-of-service (DoS) attacks pose significant challenges to system stability and performance.
• Asynchronous dynamics between system and controller modes require specialized modeling.

Purpose of the Study:

• To investigate the asynchronous non-fragile H∞ control problem for MJSPSs with time-varying delays.
• To design a robust controller capable of handling disturbances from quantization and DoS attacks.
• To ensure stochastic finite-time exponential stability and H∞ performance.

Main Methods:

• A multi-layer structure method was employed for controller design.
• An independent Markov chain was used to model asynchronous dynamics.
• Mode-dependent Lyapunov-Krasovskii functions were constructed to derive stability conditions.

Main Results:

• Sufficient conditions were derived for stochastic finite-time exponential stability and H∞ performance.
• The controller demonstrated robustness against delay, singular disturbances, and quantization uncertainty.
• The proposed method ensures stability and performance in bandwidth-constrained network environments.

Conclusions:

• The developed asynchronous non-fragile H∞ control strategy effectively addresses challenges in MJSPSs.
• The approach validates robust stability and performance for networked control systems.
• The study provides a valuable framework for designing controllers in uncertain and dynamic environments.