Stabilization of T-S fuzzy asynchronous Boolean control networks with time delay under noise

Area of Science:

• Control Theory
• Networked Systems
• Fuzzy Logic Systems

Background:

• Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling nonlinear systems.
• Asynchronous Boolean Control Networks (ABCNs) present challenges in control design due to asynchronous updates.
• Sampled-data control introduces time delays, complicating stability analysis.

Purpose of the Study:

• To investigate the stabilization problem of T-S fuzzy ABCNs under aperiodic sampled-data state-feedback control.
• To develop sufficient and necessary conditions for the stabilization of these complex systems.
• To extend the analysis to systems with both fixed and unfixed time delays, including noise.

Main Methods:

• Conversion of the T-S fuzzy ABCN into a discrete time-delay system using semi-tensor product theory.
• Derivation of algebraic forms for augmented ABCNs.
• Development of stability conditions using various analytical approaches.
• Inclusion of noise in time-delay analysis.

Main Results:

• Sufficient and necessary conditions for the stabilization of T-S fuzzy ABCNs with fixed time delays were derived.
• Conditions were extended to address systems with unfixed time delays and noise.
• The effectiveness of the proposed methods was validated through illustrative examples.

Conclusions:

• The proposed control strategies effectively stabilize T-S fuzzy ABCNs under aperiodic sampled-data conditions.
• The developed conditions provide a robust framework for analyzing systems with time delays and noise.
• The methodology offers a superior approach compared to existing techniques for ABCN stabilization.