Nonsynchronous Model Reduction for Uncertain 2-D Markov Jump Systems.

Area of Science:

• Control Theory
• Systems Engineering
• Stochastic Systems

Background:

• Mode information is crucial for Markov jump systems (MJSs).
• Incomplete mode information can lead to nonsynchronization problems in MJSs.
• H∞ model order reduction is vital for simplifying complex systems while maintaining performance.

Purpose of the Study:

• To investigate nonsynchronous H∞ model order reduction for 2-D MJSs with model uncertainty.
• To address the challenges posed by inaccessible mode information and potential nonsynchronization.
• To develop a robust method for designing reduced-order models in such systems.

Main Methods:

• Utilizing the Roesser model to characterize the 2-D system and its reduced-order counterpart.
• Employing the hidden Markov model framework to analyze the nonsynchronization phenomenon.
• Selecting appropriate Lyapunov functions to analyze stability and H∞ performance of the error system.

Main Results:

• Sufficient conditions for asymptotic mean-square stability and H∞ performance of the error system are derived.
• An efficient design method for nonsynchronous model order reduction is proposed using a projection lemma.
• The developed method effectively handles nonsynchronization issues in 2-D MJSs.

Conclusions:

• The proposed method provides a viable solution for H∞ model order reduction in 2-D MJSs with partial mode information.
• The approach ensures stability and performance guarantees even when the original and reduced-order models are not synchronized.
• Simulation results validate the correctness and effectiveness of the designed nonsynchronous reduced-order models.