Dissipative Asynchronous T-S Fuzzy Control For Singular Semi-Markovian Jump Systems.

Area of Science:

• Control Theory
• Fuzzy Systems
• Stochastic Systems

Background:

• Singular semi-Markov jump systems present control challenges due to mode-dependent dynamics and uncertainties.
• Asynchronous switching between system and controller modes complicates stability analysis and controller design.
• Dissipativity and stochastic admissibility are crucial for robust system performance in uncertain environments.

Purpose of the Study:

• To develop a dissipative asynchronous Takagi-Sugeno-Kong fuzzy control strategy for singular semi-Markov jump systems.
• To design an adaptive sliding-mode controller capable of handling actuator faults and time-varying delays.
• To ensure the closed-loop system is stochastically admissible and strictly (Q,R,S)-α-dissipative.

Main Methods:

• An adjustable quantized approach is employed to manage system uncertainties, nonlinear disturbances, actuator faults, and time-varying delays.
• An asynchronous method addresses the nonsynchronous issue between system and controller modes.
• A novel asynchronous sliding-mode controller with an output measurement quantizer is designed.

Main Results:

• Sufficient conditions derived from linear matrix inequalities guarantee stochastic admissibility and strict (Q,R,S)-α-dissipativity of the closed-loop system.
• The proposed controller ensures the reachability of the sliding-mode surface.
• Numerical examples demonstrate the effectiveness and superiority of the proposed control technique.

Conclusions:

• The developed fuzzy control approach effectively handles complex dynamics and uncertainties in singular semi-Markov jump systems.
• The asynchronous sliding-mode controller offers robust performance and adaptability to actuator faults.
• The proposed method provides a reliable framework for practical control applications requiring stability and dissipativity guarantees.