Observer-Based Security Control for 2-D Fuzzy Switched Systems With Nonhomogeneous Sojourn Probabilities

Area of Science:

• Control Systems Engineering
• Systems Theory
• Fuzzy Logic

Background:

• Two-dimensional (2-D) fuzzy switched systems (SS) are complex systems requiring robust control strategies.
• Existing Markov process frameworks can be computationally intensive and less measurable.
• Security control is crucial for these systems, especially against uncertain, randomly occurring attacks.

Purpose of the Study:

• To propose a novel framework for nonhomogeneous sojourn probabilities in 2-D fuzzy SS.
• To investigate observer-based security control for these systems under adaptive-threshold-based saturation.
• To address security control challenges posed by uncertain, norm-bounded attack rates.

Main Methods:

• Development of a nonhomogeneous sojourn probability framework.
• Design of an adaptive-threshold-based saturation function to mitigate attack effects.
• Application of Lyapunov stability theories to derive control conditions.

Main Results:

• The proposed framework enhances measurability and reduces computational complexity compared to traditional Markov processes.
• Sufficient conditions are derived to guarantee asymptotic mean square stability with noise attenuation.
• The adaptive saturation function effectively limits the impact of abnormal attacks.

Conclusions:

• The novel nonhomogeneous sojourn probability framework offers a more practical approach for 2-D fuzzy SS.
• The developed observer-based security control strategy ensures system stability and performance under uncertain attacks.
• Simulation results validate the effectiveness of the proposed theoretical framework and control methods.