Asynchronous Fault Detection Observer for 2-D Markov Jump Systems.

Area of Science:

• Control Systems Engineering
• Systems Theory
• Stochastic Systems

Background:

• Designing fault detection (FD) observers for 2-D Markov jump systems (MJSs) is challenging due to asynchronism between system and observer modes.
• Traditional FD observers often assume synchronous mode transitions, which is not always feasible in real-world MJSs.

Purpose of the Study:

• To develop an asynchronous fault detection observer design for 2-D Markov jump systems (MJSs) using a Roesser model.
• To address the challenge of asynchronous mode variations between the system and the observer.

Main Methods:

• Employed a hidden Markov model (HMM) to manage the asynchronous mode transitions.
• Formulated a multiobjective solution combining H∞ attenuation and H∞ increscent indices.
• Utilized linear matrix inequality (LMI) technology to derive sufficient conditions for asynchronous FD observer existence.

Main Results:

• Established sufficient conditions for the existence of asynchronous fault detection observers for 2-D MJSs.
• Developed an asynchronous FD algorithm to achieve optimal performance indices.
• Demonstrated the effectiveness of the proposed approach through a numerical example involving the Darboux equation.

Conclusions:

• The developed method provides a robust solution for asynchronous fault detection in 2-D MJSs.
• The use of HMM and LMI technology offers a systematic way to design high-performance asynchronous FD observers.
• The findings are validated by a practical numerical example, confirming the approach's soundness.