Observer-based H_∞ control design for singular switching semi-Markovian jump systems with random sensor delays

Area of Science:

• Control Theory
• Stochastic Systems
• System Identification

Background:

• Singular switching semi-Markovian jump systems present challenges due to uncertain transition rates and sensor delays.
• Robust control design is crucial for maintaining system stability and performance under these conditions.

Purpose of the Study:

• To design an H_∞ controller for singular switching semi-Markovian jump systems with uncertain parameters.
• To ensure stochastic stability and achieve a prescribed H_∞ performance index.

Main Methods:

• A Luenberger observer is employed to estimate system states.
• Stochastic stability analysis is performed using bounds on transition rates.
• Linear Matrix Inequalities (LMIs) are utilized to derive controller gains.

Main Results:

• Sufficient conditions for stochastic stabilizability and H_∞ performance are established.
• Controller gain matrices are determined by solving a set of LMIs.
• The effectiveness of the proposed control design is validated through a numerical example.

Conclusions:

• The developed H_∞ control design effectively addresses singular switching semi-Markovian jump systems with uncertainties.
• The LMI-based approach provides a systematic way to guarantee stability and performance.
• The results offer a valuable contribution to robust control theory for complex dynamic systems.